Topics, D
D'Alembertian / D'Alembert Operator
> s.a. causal sets [discretized]; laplacian;
types of wave equations.
* Idea: The Lorentzian geometry
version of the Laplacian operator, \(\square\) = gab
∇a∇b .
* On scalars: Can be written
as \(\square\,\phi = |g|^{-1/2} (|g|^{1/2} g^{ab}\partial_b \phi)_{,a}\) .
* In harmonic coordinates:
It simplifies to \(\square\,\phi\) = gab
∂a∂b
φ .
> Online resources:
see MathWorld page;
Wikipedia page.
DAMA and DAMA/LIBRA Experiments > see dark matter detection.
Damped Systems
> s.a. dissipation; oscillators.
* In quantum theory:
Damped systems give rise to complex spectra and corresponding resonant states.
@ Negative damping: Green & Unruh AJP(06)aug [and the Tacoma Narrows bridge].
@ In quantum theory: Caldeira & Leggett PRA(85) [effect on interference];
Chruściński JMP(03)
[resonant states and irreversibility].
> In quantum theory:
see Lindblad Equation; quantum oscillators;
states in quantum field theory; types of quantum states.
Darboux Space > see 2D geometries; 3D geometries.
Darboux Transformation
> s.a. quantum systems with special
potentials [quasi-exactly solvable]; toda lattice.
@ General references: Darboux CRAS(1882);
Rosu in(99)qp/98 [review].
@ Related topics: Bagrov et al mp/98-conf [of coherent states];
Samsomov JMP(98)qp/97 [and phase-space transformations];
Ustinov RPMP(00)mp [and solutions of differential equations].
@ Generalized: Morales et al JMP(01);
Humi NCB(02)mp [fractional];
Song & Klauder JPA(03) [time-dependent Hamiltonian systems];
Hill et al RMS(15)-a1505 [for differential operators on the superline].
> Online resources:
see Encyclopedia of Mathematics page.
Darboux's Theorem > see symplectic manifold.
Dark Energy > s.a. dark-energy equation of state; dark-energy models; observational cosmology.
Dark Matter > s.a. dark-matter detection, distribution and phenomenology, theoretical models, types; matter contents of the universe.
Dark Photons > see dark-matter detection; dark-matter types.
Data Analysis > see statistics and data analysis in physics.
Davenport Constant > see finite groups.
Davisson-Germer Experiment > see electron.
de Broglie Relation > see photons.
de Broglie-Bohm Interpretation of Quantum Mechanics > see pilot-wave interpretation.
De Donder Gauge > see gauge.
De Donder-Weyl Formalism > see types of symplectic structures.
de Finetti Theorem
@ References: Barrett & Leifer NJP(09) [for test spaces];
Christandl & Toner JMP(09);
Leverrier & Cerf PRA(09)-a0904 [quantum, phase-space representation];
Rougerie a1409-ln [and mean-field theory and Bose-Einstein condensation].
> Online resources:
see Wikipedia page.
de Groot Dual of a Topology
> s.a. causal structures in spacetime; spacetime topology.
$ Def: The de Groot dual of
a topology τ on a set X is the topology τ* whose closed
sets are generated by compact saturated subsets of (X, τ).
> Online resources:
see Wikipedia page.
de Rham Cohomology / Complex > see types of cohomology theories.
de Rham Theorem
> s.a. types of cohomology theories.
$ Def: The de Rham cohomology
H*dR(M)
is the dual of the real singular homology H*(M;
\(\mathbb R\)).
@ References: in Warner 71.
de Rham-Gabadadze-Tolley Theory
* Idea: A non-linear
massive gravity theory in which the ghost present in the Pauli-Fierz
theory is eliminated by using a special form of potential to recover
the Hamiltonian constraint; Some desired solutions of the theory
however are unstable.
@ References: de Rham et al PRL(10)-a1011;
Kodama & Arraut PTEP(14)-a1312 [stability of the Schwarzschild-de Sitter black hole];
Bernard et al PRD(15)-a1410 [linearized, massive graviton field equations on an arbitrary background].
de Sitter Spacetime > s.a. fields and particles in de sitter spacetimes.
de Sitter-Fokker Precession > see Geodetic Precession.
Debye Cutoff Length
@ References: Spiegel ap/98-fs [and gravity];
Rubab & Murtaza PS(06) [non-Maxwellian plasmas].
Debye Model > see specific heat.
Debye-Waller Factor
Decay > see particles; quantum state evolution; resonances.
Decidability
> s.a. computation [algorithmic decidability].
@ References: Paillusson & Booth a2005-FQXi [and science, historical];
Müller a2008-FQXi
[undecidability, unpredictability, and what we can know].
DECIGO (Deci-Hertz Interferometer Gravitational-wave Observer) > see space-based gravitational-wave detectors.
Decision Theory > see game.
Decoherence > s.a. decoherence in specific systems; semiclassical quantum mechanics; vacuum.
Decoherence Functional > see quantum histories.
Decoherent Histories Formulation of Quantum Theory > see quantum histories.
Decomposition of Functions and Tensors
Deconfinement > see QCD effects.
Dedekind Cut > see numbers.
Deep Inelastic Scattering > see scattering; qcd and qcd phenomenology.
Deep Learning
@ References: Garg & Ramakrishnan a2005 [quantum].
Defects (in condensed matter physics, and spacetime)
Deficit Angle > s.a. cosmic strings;
magnetic monopoles; regge calculus.
@ In spacetime:
Clifton & Barrow PRD(10)-a1001 [effects, and constraints in the Solar System].
Definitions > see mathematics.
Deformation
> s.a. Elasticity; hamiltonian dynamics [phase space];
lie algebras; Logarithms;
particle models; Planck Cube.
@ Of varieties, schemes and manifolds: Glazunov a1601 [elementary introduction, and applications];
Guan et al a1911,
a1912 [of algebraic structures].
@ And gravity / spacetime: Maia et al GRG(11) [of FLRW models];
> s.a. lorentzian metrics.
> And emergent fields / gravity:
see emergent gravity; formulations of general relativity;
gauge theories [origin]; spacetime structure [gravity as distortion].
Deformed Special Relativity > see DSR.
Degeneracy of Eigenvalues of the Hamiltonian
> s.a. quantum systems.
@ When: Fallieros & Hadjimichael AJP(95)nov;
Chau AJP(95)nov
[from supersymmetric quantum mechanics].
Degenerate Metrics > see gravity theories with extended signatures; types of metrics.
Degravitation > see brane-world gravitation.
Degrees of Freedom of a Dynamical System
@ References: Burić FP(15)-a1411 [relations between different notions].
Degree Theory in Banach Spaces
* History: Developed by Leray and Schauder in the 1930s.
@ References: Leray & Schauder AENS(34);
Rothe 86.
Dehn's Lemma
> Online resources:
see MathWorld page;
Wikipedia page.
Dehn Surfaces > see 3-manifolds.
Dehn Surgery
* Idea: An operation on3-manifolds.
@ References: Gang a1803 [algorithm].
> Online resources: see
MathWorld page;
Wikipedia page.
Delaunay Graph / Triangulation > see voronoi tilings.
Delayed-Choice Experiments > see experiments in quantum mechanics.
Delone Set
* Idea: A type of
well-spaced set of points in Euclidean space.
$ Def: A point set
S in \(\mathbb R\)d
is called a Delone set if it is uniformly discrete and relatively dense;
i.e., if there are numbers R > r > 0, such that
each ball of radius r contains at most one point of S,
and every ball of radius R contains at least one point of S
[from Tilings Encyclopedia page].
@ References: Nagai a1702
[general framework for tilings, Delone sets, functions and measures].
> Online resources:
see Wikipedia page.
Delta Function > see non-standard analysis; distributions.
Dense Subset
> see posets \ topology.
$ Def: A subset A
of a topological space X such that every open neighborhood of
x ∈ X contains an element of A.
Density, of a Graph > see graph invariants.
Density, Tensor > see tensor fields.
Density Functional Method / Theory
* Idea: An approach to
the study of properties of materials (many-particle systems) based on
the idea that they can all be derived from knowledge of the electron
density n(r) in the material, using an
appropriate functional F[n] of this density.
@ References: Kohn & Sham PR(65);
Kohn RMP(99) [Nobel lecture];
Prodan Phy(10) [use at finite temperature];
Blanchard et al IJQC(12)-a1011 [on phase space];
Capelle & Campo PRP(13) [and model Hamiltonians];
Hofer JPCS(14)-a1311 [and the future of physics];
Kvaal et al JChemP(14)-a1312 [Moreau-Yosida regularization and differentiable formulation of density-functional theory];
Zangwill a1403,
PT(15)jul [history];
Banks a1503 [for field theorists].
@ Books:
Engel & Dreizler 11;
Giustino 14.
@ Types of systems:
Koshelev a0812 [relativistic];
Meng ed-16 [for nuclear structure];
Hait & Head-Gordon JCTC(18)-a1709 [dipole moments of polar molecules];
Sanna et al PRL(20) [conventional superconductors];
Hait et al a2011 [small chemical systems].
@ And computation: Sellier & Dimov JCP(14) [Wigner Monte Carlo approach];
news pt(16)jul,
Burke Phy(17)sep [simplifying the detailed computations];
Godby Phys(20)
[extending simulations to larger length scales].
> Online resources:
see Wikipedia page.
Density Matrix
> s.a. mixed quantum states.
* Idea: An operator
ρ on the Hilbert space for a quantum system satisfying
ρ† = ρ and tr ρ = 1.
* Uses: As "statistical
mixture", "reduced density matrix", and "conditional density matrix".
* Reduced density matrix:
Given a density matrix ρ for a system, and a subsystem
identified with a subspace of the Hilbert space, the reduced density
matrix for the subsystem is the trace of ρ over the orthogonal
subspace of the Hlbert space; It can be considered the density-matrix
equivalent of the concept of marginal distribution for probabilities;
> It is used to define entanglement entropy.
@ General references: Dürr et al FP(05)qp/03,
Maroney FP(05) [Bohmian mechanics];
Tulczyjew a0711 [non-normalized, and selective measurements];
Weinberg PRA(14)-a1405 [as basis for quantum theory];
Budich & Diehl PRB(15)-a1501 [topology].
@ Conceptual: Anandan & Aharonov FPL(99) [meaning of density matrix];
Lobo et al a1110 [ontological status].
@ Measurement: Thekkadath et al PRL(16).
> Online resources:
see Wikipedia page.
Density of States
@ References: Wörner & Muñoz EJP(12) [finite-size corrections];
Mulhall & Moelter AJP(14)jul-a1406 [calculation and visualization, for simple quantum systems].
> Online resources:
see Wikipedia page.
Denumerability (R Smullyan, UM talk 2000)
* Analogy: Satan
tells a soul it will go free if he guesses (i) a positive integer, (ii) an
integer, (iii) two integers, (iv) a ratio, or (v) a real number; In which
cases does the soul know that he is not eternally damned?
Dependence > see Independence.
Dequantization
@ References: Cordero et al a1507 [for Born-Jordan quantization].
Derivation
$ Def: A linear
mapping between two vector spaces, satisfying the Leibniz rule.
Derivatives
> s.a. analysis [continuity classes]; fractional
derivatives; operators; tensor field.
* Directional derivative: It
depends on a vector field va,
v(f) = va
∂a f,
and coincides with the Lie derivative with respect to \(v^a\).
* Generalized derivation
of an algebra A: (Introduced by Bresar in 1991) A
linear mapping u: A → A such that
there exists a usual derivation d of A satisfying
the generalized Leibniz rule u(a b) =
u(a) b + a d(b)
for all a, b in A.
@ General references: Mukhopadhyay 12 [higher-order derivatives].
@ Special types: Hurley & Vandyck IJGMP(08) [D-differentiation].
@ Related topics: Gangopadhyaya & Ramsey AJP(13)apr [consequences of imprecise notation].
@ Generalizations: Penot 13 [non-smooth analysis and subdifferentials];
Heller et al CJP(13)-a1301 [generalized derivations and differential geometry, general relativity];
Moré & Wild JCP(14) [derivatives vs finite differences];
Marinho et al a2006
[Jackson and Hausdorff derivatives, and generalized statistical mechanics];
> s.a. analysis [Itō calculus].
> On a manifold:
see connection [covariant derivative];
exterior derivative; lie derivative;
Parallel Transport; Pfaff Derivative.
> Other types of situations:
see Banach Space [Fréchet derivative]; fractals.
Descriptors of a Mapping > see diffeomorphisms.
DESI (Dark Energy Spectroscopy Instrument) > see acceleration of the cosmological expansion.
Design (Argument by) > see cosmology.
Designer Gravity
* Idea: Theories in
which gravity is coupled to a tachyonic scalar with anti-de Sitter
boundary conditions.
@ References: Hertog & Hollands CQG(05)ht,
Hertog CQG(05) [stability].
Detailed Balance
* Idea: A joint
condition on the dynamics and a statistical state of a system described
by a set of states r, s, ...; States that the rate of
occurrence of any transition is the same as the rate of occurrence of
the inverse transition, or \(P_r W_{rs} = P_s W_{sr}\).
* Use: It implies that the
state is stationary, dPr/dt
= 0, from the master equation, but is not a necessary condition; Related
to reversibility.
@ General references: Evans JPA(05) [generalization for non-equilibrium states];
Colangeli et al JPA(11)-a1101 [systems driven away from detailed balance by a force].
@ Quantum detailed balance:
Duvenhage & Snyman JPA(15)-a1407 [and entanglement].
Detectors in Quantum Theory
> s.a. experimental particle physics; particle effects.
* Idea: A model for a detector
is often a point particle with internal energy levels, which can get excited
due to its interaction with a quantum field.
@ General references:
Bloch PR(67);
Bloch & Burba PRD(74) [and presence of particle];
Hinton JPA(83),
CQG(84);
Marshall FP(91)
[efficiency and fluctuations of electromagnetic field];
Marolf PRA(94)gq/93;
Bondurant PRA(04) [pointlike model];
Buscemi & Compagno PRA(09)-a0904 [in quantum field theory, and non-local correlations];
D'Auria et al PRL(11) [quantum decoherence of single-photon counters];
Brown et al PRD(13)-a1212 [beyond perturbation theory];
Bruschi et al JPA(13)-a1212;
Martín-Martínez & Louko PRD(14) [and the zero mode of a quantum field];
Martín-Martínez PRD(15)-a1509 [causality constraints];
Sriramkumar a1612-fs [review of concept and response to quantum field];
Luis & Ares a1707 [and non-classicality];
de Ramón et al a2102 [and causality];
Tjoa et al a2102.
@ Unruh-DeWitt detectors: Hümmer et al PRD(16)-a1506 [for fermionic and bosonic fields, renormalized];
Cong et al a2009 [inside rotating shells];
Burbano et al JHEP(21)-a2012 [path integral formalism].
@ Other models, examples:
Wick a1901 [model for real position measurements];
Yang & Jacob JAP(19)-a1905 [using first-order quantum phase transitions];
Nehra & Jacob a1909 [Wigner functions];
Teufel & Tumulka a1912 [detectors as absorbing boundary conditions];
Ballesteros et al CMP(21)-a2007 [appearance of particle tracks];
Adjei et al PRA(20)-a2001 [simulation with non-linear optics];
Iyer et al a2104
[unified formalism for spacelike and timelike events, correlations].
@ Time of detection: Brunetti & Fredenhagen PRA(02)qp/01;
Tumulka a1601,
a1601,
a1601 [time distribution of clicks].
@ Accelerated:
Klyshko PLA(91);
Sriramkumar & Padmanabhan CQG(96) [finite-time];
Davies et al PRD(96)gq [rotating];
Kim PRD(99) [accelerated oscillator];
Sriramkumar gq/01 [accelerated (D+1)-dimensional];
Sonego & Westman CQG(04)gq/03 [and geodesic motion];
Lin & Hu PRD(06) [vacuum fluctuations to radiation];
Louko & Satz JPCS(07)gq/06 [with regularisation];
Costa & Piazza NJP(09)-a0805 [and Unruh effect];
Kothawala & Padmanabhan PLB(10)-a0911 [time-dependent acceleration];
Thoma a1305
[quantum-field-theoretical model, for Unruh effect];
Anastopolos & Savvidou GRG(14)-a1403 [detection rates along non-inertial trajectories];
Doria & Muñoz a1503
[non-uniformly accelerating observers do not see a thermal state];
Costa a2008 [finite time interval, decoherence];
> s.a. mirrors.
@ In non-trivial spacetimes: Langlois AP(06) [topologically non-trivial];
Hodgkinson PhD(13)-a1309 [curved-spacetime quantum field theory];
Ng et al PRD(16)-a1606,
a1706 [and the non-local structure of spacetime];
Martín-Martínez et al PRD(20)-a2001 [fully covariant smeared particle detectors in curved spacetimes].
> Related topics:
see bell inequalities [detection loophole]; measurement
in quantum theory; unruh effect.
Determinant > see operations on matrices [including functional].
DGP (Dvali-Gabadadze-Porrati) Models >see brane cosmology.
Diagonalization > see operations on matrices; matrices [Jordan normal form].
Diagram
* In category theory:
Any collection of objects connected by morphisms.
Diagrammatic Methods in Mathematics
> Lie group / Lie algebra theory:
see Dynkin Diagram; Young Tableau.
> Combinatorics /
discrete structures: see Hasse
Diagram [poset theory]; Schlegel
Diagram; Venn Diagram [set theory].
> Other mathematical
areas: see characteristic
polynomials; embedding; exact
sequence; Greechie Diagram; knot
theory; voronoi tiling.
Diagrammatic Methods in Physics and Related Areas
> Quantum field
theory: see quantum field theory formalism
(and Feynman Diagram); fermions
[fermion algebra]; generalized field theories.
> Other quantum theory:
see axioms for quantum theory; path integrals;
quantum information.
> Gravitational theories:
see einstein's equation [perturbative method];
lovelock gravity; Penrose Diagram;
Spacetime Diagram.
> Other physics,
specific diagrams: see Free-Body
Diagram; Krajewski Diagram
[standard model]; Phase Diagram.
> Other physics, techniques:
see heat kernel; non-commutative
gauge theories; scalar fields
[perturbative expansion of path integrals].
> Astronomy: see
HR Diagram, Hubble
Diagram [these are actually plots rather than diagrams].
Diamagnetism > see magnetism.
Diameter > see metric spaces.
Diamond-Shaped Regions > see under Alexandrov Sets.
Dichroism > see polarization.
Dicke Model
* Idea: A
collection of two- and three-level atoms interacting with (a single
quantized mode of) the electromagnetic field and contained within a
volume much smaller than the smallest resonance wavelength; It has a
phase transition with the atom-field coupling as control parameter.
@ General references:
Buzek et al PRL(05)qp [ground-state instabilities];
Dimer et al PRA(07)qp/06 [realization in cavity QED];
Garraway PTRS(11);
Bastarrachea-Magnani & Hirsch RMF-a1108 [numerical solutions];
Bhaseen et al PRA(12)-a1110 [dynamics of non-equilibrium Dicke models];
Hirsch et al AIP(12)-a1110 [mean-field description];
Braak JPB(13)-a1304 [N = 3, solution];
Kirton et al a1805-AQT [intro].
@ Critical behavior: Castaños et al PRA(12)-a1206;
Bastidas et al PRL(12) [non-equilibrium quantum phase transitions];
Dey et al PRE(12)-a1208 [information geometry, quantum phase transitions];
Nahmad-Achar et al PS(13) [catastrophe formalism and group theory];
Bastarrachea-Magnani et al PRA(14) [density of states and excited-state quantum phase transitions],
PRA(14) [chaos and regularity, quantum and semiclassical];
del Real et al PS(13)-a1409 [Husimi distribution and Wehrl entropy];
Bhattacherjee PLA(14) [non-equilibrium dynamical phases];
Bastarrachea-Magnani et al PRE(16)-a1509 [regular and chaotic regions in phase space].
@ Generalized: Aparicio et al a0706 [generalized fermion, phase transition];
Grinberg AP(11) [non-classical effects].
> Properties,
related concepts: see Fisher Information.
> Related models:
see Tavis-Cummings Model.
Dicke States > s.a. entanglement measures.
* Idea: Multi-particle
states of spin-1/2 particles with the maximal value of the total
angular momentum; They were proposed by Dicke in 1954 and have
become important more recently in quantum information theory.
@ References: Dicke PR(54);
Liu & Hu a1511
[in high spin multi-particle systems].
Dickey Bracket > see lagrangian dynamics.
Dielectrics / Dielectric Constant > see electricity [conductivity]; electromagnetic fields in matter.
Difference Equations
@ General references: Lakshmikantham & Trigiante
02 [including numerical];
Elaydi 05 [II/III, introduction];
Zharinov TMP(11) [symmetries and conservation laws].
@ Techniques: Legault & Senior JMP(02) [second-order];
Ablinger et al a1601 [coupled systems].
@ Special types: Krichever mp/04 [rational and elliptic coefficients];
Sasaki JMP(07)-a0708,
Odake & Sasaki JMP(07)-a0708 [quasi-exactly solvable];
Ramani et al JPA(09) [integrable];
Levi & Rodríguez JPA(10) [λ-symmetries];
Iglesias et al a1011 [in implicit form].
Difference Operator > see sequences.
Differentiable Functions and Maps
Differentiable Manifolds > s.a. diffeomorphisms.
Differentiable Structure > see differentiable manifolds.
Differential Algebra
@ References: Pommaret a1707 [and mathematical physics].
Differential Equations > s.a. ordinary differential equations; partial differential equations.
Differential Group
$ Def: An \(R\)-module
generated by the elements 1 and \(d\), such that \(d^2 = 0\) with
\(R = \{m + nd \mid m,\, n \in {\mathbb Z}\}\), i.e., an abelian group
\(A\) with a nilpotent homomorphism \(d: A \to A\).
Differential Operator > see under Derivative.
Differential Space
* History:
Developed to describe Brownian motion.
@ References: in Paley & Wiener 34, ch9;
Wiener & Siegel PR(53),
NC(55) [in hidden variable theory].
Differential Topology > see differentiable manifolds.
Diffiety
* Idea: Diffieties
formalize geometrically the concept of differential equation.
@ References: Vitagliano JGP(11)-a1104 [Hamilton-Jacobi diffieties].
Diffraction > s.a. radiation [diffraction radiation].
Digamma Function
@ References: Coffey a1008 [series and integral representations].
> Online resources:
see MathWorld page;
Wikipedia page.
Digraph > see graph types.
Dilation of a Map between Metric Spaces > see distance.
Dilaton Field / Gravity > s.a. scalar-tensor gravity.
Dilogarithm Function (a.k.a. Spence's Function)
> Online resources:
MathWorld page;
Wikipedia page.
Dimensional Analysis
> s.a. thermal radiation [example of
use of pi-invariants and Buckingham's theorem].
@ References: Misic et al EJP(10) [and the Buckingham theorem];
Bolster et al PT(11)sep;
Jonsson a1408 [theoretical framework and practical algorithm];
Robinett AJP(15)apr [methodology, examples, power and limitations];
Lemons 17.
Dimensional Reduction > see gauge theories; spacetime dimensionality.
Dimensional Regularization Scheme > see regularization.
Dimer Models
* Dimer: In chemistry, a dimer
is a structure formed from two similar sub-units (monomers), for example a
diatomic molecule; Formally, a dimer is an edge in a perfect matching of edges
and vertices in a finite, connected graph, i.e., a set of edges such that
each vertex is adjacent to exactly one one of those edges (not all graphs
have perfect matchings).
* Applications: Dimer models were
introduced to model the physics of resonating valence bond states in lattice
spin systems.
* And integrable systems:
A correspondence between dimer models and integrable systems was introduced
by Goncharov and Kenyon; Dimer models give rise to relativistic integrable
systems that match those arising from 5-dimensional N = 1 gauge
theories studied by Nekrasov.
@ General references: Kenyon math/03-ln [intro];
Moessner & Raman a0809-ln [intro];
Cimasoni a1409-ln [geometry];
Bocklandt BLMS(16)-a1510 [recent developments];
Nash & O'Connor a1612 [geometrical approach].
@ Related topics: Cislo PhyA(08) [and the Ising model];
Eager et al JHEP(12)-a1107 [and integrable systems];
Ambjørn et al JPA(14) [on a 2D random causal triangulation];
Flicker et al PRX(20)-a1902 [on rhombic Penrose tilings];
> s.a. Rokhsar-Kivelson Point.
Diophantine Analysis / Equations
> s.a. number theory.
* Idea: Equations
with more than one independent variable and integer coefficients,
for which integer solutions are desired.
@ References:
Pillay BAMS(97),
erratum BAMS(98) [and model theory];
Shimura BAMS(06) [quadratic];
Andreescu et al 10 [II].
Diophantine Approximation
* Idea: The problem
of approximating a real number by rational numbers.
Diophantine Geometry > see geometry.
Dipoles, Dipole Moments > see atomic physics [electric]; electromagnetism with matter; gas [dipole gas]; Magnetic Dipole Moment; multipoles.
Dirac Bracket > s.a. constrained
systems and types of constrained systems [second-class].
* Idea: The pullback of the
Poisson brackets (symplectic form) to the constraint surface in phase space.
@ General references:
Bergmann & Goldberg PR(55) [and phase space transformations].
@ Modifications:
Krivoruchenko et al PRD(06)ht/05 [Moyal-like quantum deformation];
Kanatchikov a0807-proc
[generalization in the De Donder-Weyl Hamiltonian formalism].
> Online resources:
see Wikipedia page.
Dirac Cone
* Idea: A characteristic
feature in the electronic band structure of graphene.
Dirac Conjecture > see types of constrained systems [1st-class].
Dirac Delta Function > see distribution.
Dirac Equation / Fields / Theory > s.a. dirac equation in curved spacetime; generalized dirac fields; quantum dirac fields.
Dirac Hole / Sea
> s.a. quantum field theory [pilot-wave theory]; vacuum.
* Idea: A model for
the vacuum in which a positron is seen as a hole in an infinite set
of otherwise filled states of negative energy.
* Remark: Dirac's hole theory
and quantum field theory are usually considered to be equivalent.
@ For bosons: Finster ATMP(98)ht/97 [with external fields];
Nielsen & Ninomiya ht/98,
PTP(05)ht/04,
PTP(05)ht/04;
Habara et al ht/05,
PTPS(07)ht/05 [and supersymmetry];
Habara et al IJMPA(08)ht/06 [new formulation of quantum field theory],
IJMPA(08)ht/06 [renormalization method].
@ And quantum field theory: Jackiw ht/99-in [physical consequences];
Coutinho et al CJP(02)qp/00;
Solomon CJP(03)qp/02,
qp/03,
ht/04-ch,
CJP(05)qp;
Moffat PLB(05)ht [for gravity, and the cosmological constant];
Esposito FP(06)
= FP(07) [Majorana manuscript];
Finster & Grotz JMP(10) [and causal perturbation expansion];
Dimock LMP(11)-a1011 [alternative construction].
> Online resources:
see Wikipedia page.
Dirac Manifolds
@ References: Bursztyn a1112-ln.
Dirac Matrices > see under Gamma Matrices.
Dirac Monopoles > see monopoles.
Dirac Oscillator
* Idea: An interacting system
of a relativistic massive fermion under the action of a linear potential.
@ References: Martínez-y-Romero et al EJP(95)qp/99;
Alhaidari IJTP(04)ht [Green function];
de Lima PLA(08)-a0707;
Sadurní et al JPA(10)-a0902 [coupled to an external field];
Quimbay et al EJTP(14)-a1201 [canonical quantization, in 1+1 and 3+1 dimensions];
Franco-Villafañe et al PRL(13)-a1306
[experimental realization];
de Castro a1906
[as a spin-1/2 fermion in a transverse homogeneous magnetic field];
Montañez & Quimbay a2005 [different spatial dimensionalities];
> s.a. green function.
@ In 2+1 dimensions: Andrade & Silva EPL(14)-a1406;
Menculini et al PRD(15)-a1411 [with minimal length, quantum phase transitions].
@ And minimal length: Benzair et al JMP(12) [with GUP, path integral];
Boumali et al APPB(16)-a1511 [thermal properties];
Valtancoli JMP(17)-a1611.
Dirac Quantization of Constrained Systems
Direct-Action Theories > see under Action at a Distance.
Direct Limit > see limits.
Direct Product > see categories; manifolds.
Direct Sum > see categories; modules.
Directed Graph > see types of graphs.
Directed Set > see set theory.
Dirichlet Eta Function
* Idea: A special
function, a.k.a. alternating zeta function.
@ References: Milgram JoM(13)-a1208 [integral and series representations].
Dirichlet Problem
* Idea: A
boundary-value problem, in which one looks for a solution to an elliptic
partial differential equation, given the value on the boundary.
Dirichlet Space
* Idea: One of the three
fundamental Hilbert spaces of holomorphic functions on the unit disk.
@ References: El-Fallah et al 14.
Disaster Scenarios > see black-hole formation.
Discernibility of Particles > see particle descriptions.
Disclination > see defects.
Disconnected Set > see connectedness.
Discord > see quantum discord.
Discovery
@ References: Loeb a1207 [nurturing scientific discoveries];
Gilead a1402 [discovery of actual vs possible entities];
Peiris a1410-IAU [anomalies and discoveries in cosmology];
Wells a1904 [in high energy physics].
Discrete Geometry > see geometry; combinatorial geometry; discrete spacetimes.
Discrete Groups > see finite groups.
Discrete Mathematics
> s.a. combinatorics;
computation; number theory;
proof theory; set theory.
@ References: Penner 99 [II].
Discrete Models / Systems in Physics
> s.a. Continuum; discrete geometries;
time in physical theories.
@ General references: Easton 98 [geometric methods];
Kornyak in(09)-a0906 [gauge invariance and quantization],
in(10)-a1006 [structure and symmetries];
Khare et al Pra(12)-a1111 [solutions in terms of Lamé polynomials];
Kornyak PPN(13)-a1208 [discrete gauge connections, origin of quantum behavior];
Navascués et al JPA(13)-a1110
[spectra of coarse-grained variables based on a collection of microscopic variables];
Marrero et al a1303 [local description];
Kornyak MMG-a1501
[combinatorics, statistics and continuum approximations].
@ Matter fields: in da Paz et al PLA(14)-a1406 [granularity of the electromagnetic field].
@ Condensed-matter-inspired models: Tahim et al MPLA(09)-a0705 [deformable solid];
't Hooft IJMPA(09) [4D crystal with defects].
@ Continuum limit:
Bergman & Inan ed-04 [continuum models];
Tarasov JPA(06) [with long-range interactions].
@ Minisuperspace models:
Gambini & Pullin PRL(03)gq/02,
CQG(03)gq/02;
Baytaş & Bojowald PRD(17)-a1611.
> Gauge theories:
see chern-simons theory; gauge
theories; lattice gauge theories;
self-dual solutions; types
of gauge theories; types of yang-mills
theories [on a complex].
> Other examples:
see Bernoulli Map; cellular automata; dirac
fields; generalized quantum field theories;
hamiltonian systems; lagrangian
systems; integrable systems; quantum
systems; Sequential Dynamical Systems; spin models;
types of wave equations.
Discrete Topology > see types of topologies.
Discretization
@ General references: Tonti JCP(14) [purely algebraic formulation of physical laws, without discretization].
@ Techniques: Seslija et al JGP(12)-a1111
[discrete exterior geometry, Dirac structures and finite-dimensional port-Hamiltonian systems];
Palha et al JCP(14) [basic concepts];
Höhn JMP(14)-a1401 [systems with temporally varying discretization, quantization];
Levi & Rodriguez a1407
[discrete variables and invariant schemes when the discrete Schwarz theorem is satisfied];
> s.a. Finite-Element Method.
> Mathematical:
see Continuum; Derivatives;
differential equations; discrete
spacetimes; distributions [Dirac delta];
laplace equation; riemannian geometry.
> Gravity-related systems:
see approaches to quantum gravity; Barrett-Crane Model
[discretized BF theory]; BF theory; bianchi models;
brane world [Randall-Sundrum models];
canonical quantum gravity models;
constraints in general relativity;
formulations of general relativity;
FLRW spacetimes; gowdy spacetimes;
lattice gravity; loop quantum gravity;
perturbations in general relativity;
riemannian geometry.
> Quantum systems:
see canonical quantum theory; formulations of quantum theory;
modified quantum mechanics; path-integral quantum mechanics;
path-integral quantum field theory; QED;
quantum chaos; types of quantum field theories.
> Other physical systems:
see computational physics; constrained systems;
Continuous Media; field theory; fluids;
graph theory in physics; modified electromagnetism;
heat equation; klein-gordon fields;
Kolmogorov System; lattice field theories;
regge calculus; types of field theories;
types of yang-mills theories; wave equations.
Disentropy
@ References: Ramos a1901 [information theory].
Disformal Interactions / Transformations
> s.a. Horndeski Action; Mimetic
Gravity; Vainshtein Mechanism.
@ General references: Brax & Burrage PRD(15)-a1407 [disformal scalars, and atomic and particle physics];
Bittencourt et al CQG(15)-a1505 [and the Dirac equation];
Fumagalli et al a1610 [as a change of units].
@ Disformal gravity: Ip et al JCAP(15)-a1507 [solar system constraints];
Sakstein & Verner PRD(15)-a1509 [Jordan-frame analysis].
@ And cosmology: Minamitsuji PLB(14) [cosmological perturbations in scalar-tensor theory];
Sakstein JCAP(14)-a1409;
Sakstein PRD(15)-a1409 [cosmological solutions];
Motohashi & White JCAP(16)-a1504 [invariance of curvature perturbations];
Domènech et al JCAP(15)-a1505;
Alinea & Kubota a2005 [primordial perturbations].
@ Other spacetimes: Anson et al a2006 [disformal versions of Kerr metric + scalar field].
Disk > see electromagnetism [charged, rotating]; gravitating matter.
Dislocation > see defects; geodesics.
Disordered Systems
> s.a. Order; quantum systems; Random
Medium; solid matter [amorphous solids, glass].
* In a solid:
Disorder has a strong influence on the solid's elastic properties;
In terms of electronic properties, disorder in a crystal tends
to localize electrons and drive a transition from a metallic to
an insulating state (Anderson localization transition).
* Remark: In quantum
statistics, disorder is described in terms of entropy and algorithmic
complexity, which is not antithetical to the notion of order.
@ General references: Binder & Kob 05,
Bovier 06 [statistical mechanics, r JSP(08)];
Sewell a0711-en [in quantum statistical mechanics, survey];
Brody et al JPCS(09)-a0901 [in thermal equilibrium];
Giacomin et al a0906 [and critical behavior];
Wreszinski JMP(12)-a1208-ln [quantum, rev].
@ Strong disorder:
Iglói & Monthus PRP(05) [RG approach];
Monthus & Garel JPA(08) [equilibrium properties and phases];
Vojta et al PRB(09)
+ Refael Phy(09)jan [RG approach, universal behavior];
Goldsborough & Evenbly PRB(17)-a1708 [entanglement renormalization].
@ In condensed matter:
Foster et al PRB(09)
+ Vojta Phy(09) [typical electron wave function];
Pollet et al PRL(09)
+ Weichman Phy(09)
[patches of order in disordered boson systems and superfluid-insulator transition];
Blundell & Terentjev PRS(11) [influence on deformations in semiflexible networks];
Briet & Savoie RVMP(12) [magnetic response];
Chern et al NJP(14) [disorder-induced criticality in artificial spin ices];
Ashhab PRA(15)-a1510 [effect on the transfer of quantum states];
Kurečić & Osborne a1809 [interacting quantum systems, stochastic integral representation];
Skinner et al PRL(21)
+ news Phys(21) [detecting hidden order].
> Related concepts / tools:
see Anderson Localization [random media];
Replica Symmetry; QCD phenomenology;
wave phenomena [propagation].
> Related phenomena:
see bose-einstein condensates; casimir
effect; localization.
Dispersion, Dispersion Relation
Dissipation, Dissipative System
Distance Function > s.a. special types and manifolds with metrics.
Distance Measurements > see Parallax; spatial geometry of the universe [in cosmology].
Distance-Redshift Relation > see geometry of the universe.
Distinguishable Particles
> s.a. Identity of Indiscernibles; Indistinguishability;
particle statistics.
* Idea: Two
particles are distinguishable if their quantum state changes under
exchange of the spatial locations of the two particles.
@ References: Marletto a2009 [and thermodynamic work extraction].
Distinguished Curves > same as unparametrized geodesics.
Distinguishing Spacetime > see causality conditions.
Distorsion / Distortion > see formulations of general relativity; spacetime structure; s.a. Deformation.
Distribution (Generalized function)
Distribution (On a manifold) > see tangent structures.
Distribution Function > see states in statistical mechanics; wigner function.
Disturbance > see uncertainty [error-disturbance relations].
Divergence of a Vector Field > see vector calculus.
Division Algebra
> s.a. Tenfold Way [real super division algebras].
$ Def: An algebra
without zero divisors, i.e., such that there do not exist a,
b ≠ 0 with ab = 0.
* Finite-dimensional
real division algebras: The Frobenius theorem states that up to
isomorphism there are exactly three such algebras, the reals themselves
(dimension 1), the complex numbers (dimension 2), and the quaternions
(dimension 4).
@ References:
Baez & Huerta in(10)-a0909 [and supersymmetry];
Wills-Toro a1007 [graded, not necessarily associative];
Baez FP(12)-a1101 [and quantum mechanics].
> Online resources:
see Wikipedia page.
Domain Theory > s.a. posets.
* Idea: Domains are
mathematical structures for information and approximation; They combine
order-theoretic, logical, and topological ideas and provide a natural
framework for modelling and reasoning about computation; The theory of
domains formalizes the intuitive ideas of approximation and convergence in
a very general way, and has proved to be a useful tool for programming
languages and other areas of computer science, and for applications
in mathematics.
Domain of Dependence, of Outer Communications > see spacetime subsets.
Domain Wall > see topological defects.
Donaldson-Thomas Theory
@ References: Meinhardt a1601 [gentle introduction].
Donaldson-Witten Theory > see 4D manifolds.
Doomsday Argument > see civilizations; cosmological singularities [cosmic doomsday].
Doppler Lensing
* Idea: The apparent
change in object size and magnitude due to peculiar velocities.
@ References: Bacon et al MNRAS(14)-a1401 [and cosmology].
Dot Product > see vectors.
Double Copy
* Idea: 2010, A correspondence
between scattering amplitudes in gravity and their gauge theory counterpart,
subsequently extended to other quantities, providing gauge theory analogues,
for example, of black holes.
@ References: Bern et al PRL(10)-a1004;
Bern et al PRD(10)-a1004;
White CP(18)-a1708 [rev].
Double Field Theory
> s.a. types of field theories.
* Idea: A concept
developed in order to make manifest the hidden O\((d,d;{\mathbb Z}\))
T-duality symmetry of string theory, and used asan effective field theory
capturing the low energy dynamics of closed strings; It is based on a
doubled spacetime with generalized coordinate transformations, which
unify diffeomorphisms and b-field gauge transformations.
@ General references: Hull & Zwiebach JHEP(09)-a0904;
Hohm & Kwak JPA(11)-a1101;
Kan et al a1201-proc [particle equations of motion];
Aldazabal et al CQG(13)-a1305 [rev];
Naseer JHEP(15)-a1508 [canonical formulation and conserved charges];
Chatzistavrakidis et al a1903-proc [algebroid structure];
Lescano & Mirón-Granese a2003 [phase space];
Alfonsi & Berman a2101 [and geometric quantisation].
@ Flux formulation: Geissbühler et al JHEP(13)-a1304;
du Bosque et al JHEP(16)-a1509.
@ Geometry: Vaisman JMP(12)-a1203;
Hohm & Zwiebach JHEP(12) [Riemann tensor],
JMP(13)-a1212 [invariant geometry];
Park JHEP(13)-a1304 [and diffeomorphisms];
Hohm et al FdP(13)-a1309 [spacetime, rev];
Blumenhagen et al JHEP(14)-a1312 [non-associative deformations];
Berman et al JHEP(14)-a1401 [global aspects];
Cederwall JHEP(14)-a1402 [metric on doubled space],
JHEP(16)-a1603 [geometry of superspace];
Hassler JHEP-a1611;
Penas FdP(19)-a1807 [generalized connection];
Berman a1903-proc [Kaluza-Klein approach].
@ Phenomenology: Wu & Yang JCAP(14)-a1307 [cosmology];
Wu & Yang a1312 [cosmological signatures];
Bekaert & Park JHEP(16)-a1605 [of higher-spin gravity];
Krasnov NPB(18)-a1803 [and the Standard Model fermions].
> Videos:
Zwiebach conf(12) [32'].
Double Layers > see gravitating matter fields.
Double Wieferich Primes > see number theory.
Double-Beta Decay
> s.a. Beta Decay [including neutrinoless]; neutrino;
types of particles [lepton number].
@ References:
Klapdor-Kleingrothaus 10;
Klapdor-Kleingrothaus & Krivosheina in(09)-a1006 [fundamental physics and cosmology].
Double-Slit Experiment > see interference.
Doubly General Relativity > see under rainbow gravity.
Doubly Special Relativity > see DSR.
Drell-Yan Process
* Idea: A high
energy hadron-hadron scattering process in which a pair of
oppositely-charged leptons is produced out of the annihilation
of a quark-antiquark pair from the two hadrons.
> Online resources:
see Wikipedia page.
dRGT Gravity Theory > see under de Rham-Gabadadze-Tolley.
Drinfel'd Doubles
@ References: Ballesteros et al JPA(07) [and Lie algebras];
Ballesteros et al CQG(13)-a1303 [for 2+1 gravity];
Ballesteros et al CQG(18)-a1809 [for the Poincaré group].
Drum > see sound; spectral geometry.
Dual Charge > see Charge.
Dualities in Field Theory > s.a. Triality.
Duality for Mathematical Structures
> see cell complex; forms [Hodge dual];
functors; operator [spaces]; posets.
> Online resources:
see Wikipedia page.
Duffin-Kemmer-Petiau Theory > see modified QED [SDKP4].
Dufour Effect > see dynamics of gravitating bodies.
Duhem-Quine Problem > see statistics.
Dulong-Petit Law > see specific heat; history of physics.
Dust > see fluid; interstellar; matter.
Dutch Book Argument
> s.a. hidden variable theory.
* Idea: An argument in the theory of probability.
> Online resources:
see Stanford Encyclopedia of Philosophy page;
Wikipedia page.
Dvali-Gabadadze-Porrati Models > see DGP Models.
Dyad > see spheres [complex dyad on 2-sphere], or vielbein in general.
Dyadosphere
* In astrophysics:
A hypothetical region around a compact object where the electric field
exceeds the critical value for rapid Schwinger pair production;
Pair production is a self-regulating process that would discharge
a growing electric field, in the example of a hypothetical collapsing
charged stellar core, before it reached 6% of the minimum dyadosphere value.
@ References: Page ap/06,
ap/06-proc,
ApJ(06)ap [self-regulation];
Cherubini et al PRD(09)-a0905 [Reissner-Nordström, "dyadotorus"];
Raychaudhuri et al MPLA(09) [test-particle motion in dyadosphere geometry].
Dynamical System > see formalism of classical mechanics.
Dynamical Triangulations > s.a. causal dynamical triangulations.
Dynamically Assisted Sauter-Schwinger Effect > see particle effects.
Dynamics
> s.a. physical theories.
* Idea: The study
of the evolution of a physical system, that can be a material object
(mechanics of particles or extended objects), a material medium (continuum
mechanics – fluid mechanics and condensed-matter physics), a field
(field theory), or some more general structure.
* Structure: It is
described in terms of physical laws and initial conditions; This dichotomy
appeared with Newton, and modern physics has extended the notion of
initial conditions to internal degrees of freedom and fields; Some
quantization methods try to overcome the distinction.
@ References: in Janssen SHPMP(09) [vs kinematics];
Spekkens a1209-FQXi
[kinematics and dynamics must yield to causal structure];
Gogioso a1501
[monadic framework, and shift from histories to dynamics];
Gallego Torromé a2007 [non-reversible].
> Related topics:
see Kinematics; Motion;
Symbolic Dynamics.
Dynkin Diagram
* Idea: A type
of diagram used to classify semisimple Lie algebras.
@ Generalized: Zuber ht/97-proc;
Keller AM-a1103
[proof of the periodicity conjecture for pairs].
> Online resources:
see Wikipedia page.
Dyon
> s.a. black-hole entropy; black-hole
solutions [diholes]; monopole.
* Idea: A particle
with both electric and magnetic charge.
* Result: In ordinary
4D field theory, it has to be structureless because there are no bound
states of an electric charge in the field of a magnetic monopole.
@ General references: Schwinger Sci(69)aug;
Teh & Wong IJMPA(06)ht/05 [SU(2) Yang-Mills-Higgs theory, 1/2 monopole charge];
Barnich & Gomberoff PRD(08)-a0705 [duality-invariant formulation, and black-hole thermodynamics];
Singh & Tripathy IJTP(13) [non-abelian, topological].
@ In Einstein-Yang-Mills theory: Bjoraker & Hosotani PRD(00)ht [4D];
Nolan & Winstanley CQG(12)-a1208 [and dyonic black holes, in asymptotically anti-de Sitter spacetime].
@ Spin and statistics:
Brandt & Primack IJTP(78);
Friedman & Sorkin PRD(79),
CMP(80);
Lechner & Marchetti JHEP(00)ht.
@ From Kaluza-Klein theory: Davidson & Davidson PRD(86).
Dyson Gas
* Idea:
A 2D gas of Coulomb charges in a background potential.
@ References: Zabrodin CAOT(10)-a1002 [canonical and grand canonical partition functions].
Dyson Spheres > see civilizations.
Dyson-Schwinger Equation > see under Schwinger-Dyson.
main page
– abbreviations
– journals – comments
– other sites – acknowledgements
send feedback and suggestions to bombelli at olemiss.edu – modified 21 apr 2021