Topics, V

Vacuum > s.a. vacuum phenomenology [including energy sequestering].

Vaidya Metric > s.a. black-hole solutions and thermodynamics; censorship [Vaidya-de Sitter]; gravitational collapse; spinning particles.
* Idea: A metric describing the gravitational collapse of a finite shell of incoherent radiation falling into flat spacetime and giving rise to a Schwarzschild black hole.
* Line element: In usual radiation coordinates, given by [in the generalized one, M = M(v, r)]

ds2 = 2c dr dv − [1−2M(v)/r] dv2 + r22 .

@ General references: Denisova & Zubrilo G&C(00) [radial geodesics]; Singh & Vaz PLB(00) [quantum scalar field]; Girotto & Saa PRD(04)gq [double null coordinates]; Krisch & Glass JMP(05)gq [energy transport]; Ben-Dov PRD(07)gq/06 [outer trapped surfaces]; Bengtsson & Senovilla PRD(09)-a0809 [closed trapped surfaces]; Chirenti & Saa CQG(12)-a1201 [double-null formulation]; Berezin et al CQG(16)-a1603 [maximal analytical extension].
@ Quasinormal modes: Shao et al PRD(05)gq/04; Abdalla et al PRD(06)gq; Chirenti & Saa JPCS(11)-a1012.
@ Other perturbations: Nolan & Waters PRD(05)gq [self-similar, even perturbations]; Nolan CQG(07)gq/04 [self-similar]; > s.a. metric matching.
@ Particle motion: Bini et al CQG(11)-a1408 [effect of radiation flux].
@ Charged: Ibohal & Kapil IJMPD(10)-a1001 [Reissner-Nordström-Vaidya and Kerr-Newman-Vaidya solutions]; Chatterjee et al GRG(16)-a1512 [and the weak energy condition].
@ More general solutions: Hughston IJTP(71) [including vacuum metrics without symmetry]; Wang & Wu GRG(99)gq/98; in Joshi & Dwivedi CQG(99)gq/98; Saa PRD(07)gq [N-dimensional, + cosmological constant]; Mkenyeleye et al PRD(14)-a1407 [gravitational collapse]; Böhmer & Hogan MPLA(17)-a1710 [rotating, Kerr-like]; > s.a. Tolman Solutions.
@ More general matter: Gair CQG(02) [anisotropic pressure].
@ In Lovelock gravity: Cai et al PRD(08)-a0810; Rudra et al ASS(11)-a1101 [gravitational collapse].
@ In other modified gravity theories: Mehdipour CJP(12)-a1212 [non-commutative]; Ruan PRD(16)-a1512 [cubic gravity].
@ Related topics: Venditti & Dyer CQG(13)-a1201 [particle detector response].

Vainshtein Mechanism > s.a. Horndeski Action; massive gravity; Screening.
* Idea: An effect which plays a crucial role in massive gravities and related theories such as Galileons and their extensions; It is conjectured that this mechanism, also known as k-mouflage, allows to hide via non linear effects (typically for source distances smaller than a so-called Vainshtein radius which depends on the source and on the theory considered) some degrees of freedom whose effects are then only left important at large distances, e.g., for cosmology; It has been shown to work, e.g., for spherically symmetric, stationary situations.
@ General references: Babichev & Deffayet CQG(13)-a1304 [introduction]; Koyama & Sakstein PRD(15)-a1502 [astrophysical probes]; Winther & Ferreira PRD(15)-a1505 [beyond the quasi-static approximation]; Karwan et al a1606 [in general disformal gravity theory].
@ Cosmology and astrophysics: de Rham et al PRD(13)-a1208 [in binary pulsars]; Falck et al JCAP(14)-a1404 [cosmic web morphology]; Koyama & Sakstein PRD(15)-a1502 [astrophysical probes]; Kase et al PRD(16)-a1510 [theories beyond Horndeski].

Valence of a Tensor Field
* Idea: Its index structure, or number of vector and covector fields it acts on to produce a scalar.

van Dam-Veltman-Zakharov Discontinuity > s.a. Pauli-Fierz Theory.
* Idea: A theoretical argument requiring that the mass of the graviton be exactly zero, since otherwise measurements of the deflection of starlight by the Sun and the precession of Mercury's perihelion would conflict with their theoretical values.
@ References: Carrera & Giulini gq/01 [m > 0, with electromagnetism]; Sato ht/05 [formulation with smooth m = 0 limit]; in Eckhardt et al NA(10)-a0909.

van der Waals Fluid / Force / Equation of State > s.a. Induced Gravity; QCD phenomenology [for gluonic forces].
* Idea: A phenomenological equation of state for a non-ideal gas, proposed by Johannes Diderik van der Waals in the late 19th century, which includes the effects of a force representing the interaction between neutral molecules in a gas, decreasing faster than r−2 (higher-multipole components of the electric force); It contains a term corresponding to long-range attraction and one corresponding to short-range repulsion (> see Lennard-Jones Potential).
* Equation of state: Of the form (p + a/v2)(vb) = RT, where v = V/n is the molar volume, and a and b two parameters.
* Applications: Van der Waals forces are the dominant interactions between neutral particles on nanometer-to-micrometer length scales; They are responsible for the action of detergents, the self-assembly of viruses, and the ability of geckos to climb flat surfaces; Apparently spiders walk upside down on any surface using van der Waals forces [@ news pw(04)apr].
@ General references: in Reif 65, p173, p425; Holstein AJP(01)apr; Sambale et al PRA(07)qp/06 [local-field corrected]; Yannopapas & Vitanov PRL(07) [between macroscopic objects, first-principles theory]; Román-Velázquez & Sernelius JPA(08)-a0710 [effect of structure and geometry]; Milton et al a0811 [from multiple scattering]; Yonezawa PTP(09)-a0904 [from boundary conditions]; Liu et al EJP(10) [relationship with ideal gas]; Milton AJP(11)jul-a1101 [resource letter]; Quevedo & Ramírez a1205 [thermodynamics, geometric approach]; Caimmi a1210 [historical review]; Weidemüller Phy(13) [on a recent direct measurement]; Swendsen AJP(13)oct [thermodynamic properties, numerical approach]; Ipsen & Splittorff AJP(15)feb-a1401 [1D, 2D and 3D, pedagogical]; Klimchitskaya & Mostepanenko SPBPU(16)-a1507 [intro and recent results].
@ Critical behavior: Barra & Moro AP-a1412 [exact mean-field partition function].
@ Specific types of systems: Huttmann et al PRL(15) [controlling the van der Waals attraction between a graphene sheet and molecules by doping]; Ajayan et al PT(16)sep [2D, monolayers]; Jentschura & Debierre PRA(17)-a1705 [interaction of an excited-state atom with a ground-state atom].
@ For a quantum gas: Bärwinkel & Schnack PhyA(08) [non-ideal quantum gas]; Deeney & O'Leary EJP(12) [dilute boson gas].
@ Moving systems / retarded potential: Wu et al PRA(02) [fluctuations]; Miyao & Spohn JMP(09)-a0901 [leading term in 1/R expansion]; Noto & Passante PRD(13)-a1304 [two atoms moving with uniform acceleration]; Giovannini PRD(15)-a1506 [relativistic]; Donaire & Lambrecht PRA(16)-a1509 [velocity-dependent force on an excited atom].
@ Other applications: Jantsch et al IJMPD(16)-a1601 [role in cosmology].
> Online resources: see Wikipedia page.

Van Hove's Theorem > see representations of quantum mechanics.

Van Kampen's Theorem > see under Seifert-Van Kampen Theorem.

Van Leeuwen's Theorem
* Idea: The statement that the phenomenon of diamagnetism cannot occur in classical statistical mechanics.

Van Vleck Determinant

Variational Methods / Principles > s.a. variational principles in physics; schrödinger equation.
@ References: Giusti 03 [direct methods]; Pasicki T&A(12) [and a stronger form of the Caristi and Takahashi fixed point theorems]; Adamyan & Sushko a1306-text; Voicu & Krupka JMP(15)-a1406 [turning a non-variational system of differential equations into a variational one]; Dacorogna 14 [introduction]; Chang 16 [lecture notes].

Variational Quantum Tomography (VQT) > see quantum states.

Variational Tricomplex > see symmetries.

Variety > see Wikipedia page.

Varifold > see types of manifolds [generalizations].

Varying Speed of Light > see varying constants.

Vassiliev Invariants > see knot invariants.

Vectors [including vector space, vector algebra]

Vector / Vector-Tensor Theories of Gravity > see theories of gravity.

Vector Calculus

Vector Field

Veiled General Relatvity > see modifications of general relativity.


Venn Diagram > s.a. thermodynamics.
* Idea: A type of diagram used in set theory to show the inclusion and intersection properties among elements of a finite collection of sets.
> Online resources: see Wikipedia page.

Verifiability of a Theory > see criteria for physical theories.

Veronese Web > see Web.

Vertex Algebras
@ References: Bakalov & Nikolov JMP(06) [in higher dimensions].

Vertical Tensor Field > see vector field.

Very Special Relativity
* Idea: A theory of relativity based on a small subgroup of the Lorentz group (the subgroup T(2) of parabolic transformations within the Special Euclidean group SE(2) obtained as the stabilizer of a null vector in Minkowski spacetime, extended to include either parity or time reversal) [from Wikipedia]; It maintains the main features of special relativity but breaks rotational invariance, so it breaks Lorentz symmetry in a very mild way.
@ General references: Cohen & Glashow PRL(06) [proposal]; Sheikh-Jabbari & Tureanu PRL(08) [non-commutative spacetime realization]; Ahluwalia & Horvath JHEP(10)-a1008 [Lorentz symmetries for the standard model, VSR for the dark sector]; Das et al PLA(11)-a1004 [and non-commutative spacetime].
@ Curved spacetime version: Mück PLB(08)-a0806; Kouretsis et al PRD(09)-a0810 [Finsler geometry and cosmology].
@ Phenomenology: Das & Mohanty MPLA(11)-a1007 [incompatibility with Thomas precession]; Romero et al MPLA(13)-a1203 [equivalence to relativistic particle in a gauge field]; Alfaro & Rivelles PRD(13) [non-abelian fields], PLB(14)-a1306 [spinning particle]; Lee PRD(16)-a1512 [effect on quantum field theory]; > s.a. born-infeld electrodynamics.
> Online resources: see Wikipedia page.

Vibrations > see oscillator.

Vielbein, Vierbein > see tetrad.

Viète Formulas > see algebra.

Vietoris Topology > see types of topologies.

Vietoris-Rips Complex > a type of abstract simplicial complex.
@ References: Attali et al CG(13) [and shape reconstruction].
> Online resources: see Intelligent Perception page; Wikipedia page.

VIP (Violation of the Pauli Exclusion Principle) Experiment > see spin-statistics.

Virasoro Algebra > s.a. diffeomorphisms [Witt algebra].
* Idea: The central extension of the Lie algebra of Diff(S1).
$ Def: A Lie algebra with generators which, for the open string, is the Witt algebra with an anomalous term (depending on spacetime dimension),

[Ln, Lm] = (nm) Ln+m + c (n2 −1) δn+m, 0 .

* Representations: One is interested in finding representations for the quantization of string theory; One normally demands that all generators be represented as positive-definite Hermitian operators, in which case consistency then restricts the dimensionality, but there are many anomaly-free representations in which L0 is not positive-definite; This is not a problem, since L0 is a constraint anyway.
@ General references: Goddard & Olive ed-88; Germoni LMP(01) [classification of representations]; Wassermann a1004-ln; Iohara & Koga 11 [representations]; Schlichenmaier a1111 [second cohomology]; Gómez et al JGP(12) [geometric approach]; Zhdanov & Huang a1310 [inequivalent realizations].
@ Deformations: Bouwknegt & Pilch CMP(98); Gieseker m.QA/99 [from Toda and KdV], JDG(03).
@ Generalized to higher dimensions: Larsson in(04)-a0709 [and quantum gravity]; Gurau NPB(11).
@ Related topics: Milas CMP(04)m.QA/03 [and Ramanujan's "Lost Notebook"]; Kitölä & Rideout JMP(09)-a0905 [staggered indecomposable Virasoro modules].

Virasoro Group
@ References: Kontsevich & Suhov mp/06 [Malliavin measures].

Virial Coefficients / Expansion > s.a. Equation of State; Mayer Cluster Expansion; statistical-mechanical systems.
* Idea: The coefficients and series one gets expanding the pressure equation of state for any gas in powers of the number density n, of the form

p = kT [n + B2(T) n2 + B3(T) n3 + ...] .

* Values: For an ideal gas all virial coefficients B2 = B2 = ... = 0, and at sufficiently low densities any gas behaves that way.
* Method: The virial coefficients can be calculated as sums over labeled 2-connected graphs.
@ General references: Bhaduri et al JPA(10); Kaplan & Sun PRL(11) [new field-theoretic computation method]; Jansen JSP(12) [at low temperatures, interpretation of the radius of convergence]; Tate JSP(13)-a1303 [cluster expansion bounds on the virial expansion]; Procacci & Yuhjtman LMP(17)-a1508, Procacci JSP-a1705 [bounds for the radius of convergence].
@ Expansion in terms of 2-connected graphs: Androulaki et al JPA(10) [method for graph construction]; Tate AIHP(15)-a1402.
@ For ideal gases: Liu PRP(13) [cold fermion gas]; Olaussen & Sudbø RNSSL-a1502 [ideal quantum gases in arbitrary dimensions].
@ Other specific systems: Gavrilik & Mishchenko UJP-a1312-proc, PRE(14)-a1409 [composite, interacting bosonic particles]; Brydges & Marchetti a1403 [gas of particles with uniformly repulsive pair interaction]; Jansen JSP(15)-a1503 [multi-species Tonks gas]; > s.a. gas [cold fermion gas].

Virial Theorem > s.a. energy.
* In classical physics: The relationship between the time average of the kinetic energy of a system of mass points and the virial of Clausius; When averages are taken over a period (or, for non-periodic motion, over a long time),

avg{K} = −\(1\over2\)avg{∑i Fi · ri} ;

It is very useful in the kinetic theory of gases, e.g., to derive Boyle's law.
* In relativistic physics: The tensor virial theorem states that, for a system with vanishing stresss-energy outside a bounded V,

t2 d3x T 00 x i x j = 2 d3x T ij .

@ General references: in Goldstein 80; Milgrom PLA(94)ap [from action principle]; Böhmer et al JCAP(08)-a0710, Sefiedgar et al PRD(09)-a0908 [in f(R) gravity]; Amore & Fernández EJP(09)-a0904 [in non-linear problems]; > s.a. MOND.
@ In relativistic physics: in Schutz 85, ex.4.23; Lucha & Schöberl PRL(90); Gourgoulhon & Bonazzola CQG(94); Bonazzola & Gourgoulhon CQG(94); Nowakowski et al PRD(02) [with a cosmological constant]; Georgiou CQG(03) [rotating charged pfluids in general relativity]; Tan AP(08) [generalized, for two-component Fermi gas]; Sefidgar et al PRD(09)-a0908 [for f(R) gravity]; Roshan CQG(12)-a1208 [parametrized post-Newtonian]; Javadinezhad et al PRD(16)-a1510 [for cosmological structures]; Mashhoon Univ-a1512 [in non-local Newtonian gravity].
@ Generalizations: Georgescu & Gérard CMP(99) [in quantum physics]; Cariñena et al JPA(12)-a1209 [geometric approach]; Sukumar a1410.

Virtual Knot Theory > see knot theory.

Virtual Particles > s.a. photons; vacuum [zero-point fluctuation].
* Idea: Points in momentum space that are included in a sum over 4-momenta for intermediate states in a Feynman diagram / quantum amplitude; They do not need to lie on the mass shell, but they must be related to other 4-momenta in the process by conservation laws.
* Analogy: Like spray around a turbulent waterfall; A more precise classical analog are evanescent wave solutions of wave equations.
@ General references: in Rubbia & Jacob AS(90) [a description as good as most]; de la Torre a1505 [and the quantum field theory interpretation of quantum mechanics]; Malyshev PIT(16)-a1605 [and the Newtonian trajectories of classical physics].
@ Related topics: Nimtz FP(09)-a0907 = FP(10) [macroscopic analog]; > s.a. wave phenomena [evanescent waves].

Virtual Work > see noether's theorem [generalized].

Viscoelasticity > s.a. Elasticity; fluids.
* Examples: Viscoelastic fluids include "complex" (non-Newtonian) fluids, "squishy" or "gooey" ones like pudding, blood, the Earth's mantle, toothpaste, ketchup and gelatin, for which viscoelasticity depends, in a mathematically complex way, on the magnitude of the applied force.
@ References: Pipkin 86; news pn(07)may [viscoelastic fluid that tears]; Khair & Squires PRL(10) [technique to measure normal stress coefficients].
> Online resources: see Wikipedia page.


Visscher Basis
* Idea: The functions Ψlmn:= (x/a)l (y/b)m (z/c)n, where l, m, and n are positive integers, which are not orthonormal, but in terms of which one can decompose functions on \(\mathbb R\)3 – The expansion is related to a Taylor series expansion around x = y = z = 0.

Visualization > s.a. computational physics.
@ References: Goodwin PhSc(09)jul [visual representations and truth-bearing role].

Vlasov Equation > s.a. stochastic processes; magnetism [plasma physics]; solutions of einstein's equation with matter [Einstein-Vlasov system].
* Idea: A differential equation describing the time evolution of the distribution function of a plasma consisting of charged particles with long-range interactions.
> Online resources: see Wikipedia page.

Vlasov-Poisson Equations / System
@ References: Esen & Gümral a1203 [and differential geometry]; Lazarovici & Pickl a1502 [mean-field limit].

Void (in Cosmology) > see galaxy distribution [the void phenomenon]; milky way galaxy [Local Void]; theories of cosmological acceleration.

Volume > s.a. form [volume form]; geometrical operators in quantum gravity.
@ Spacetime volume: Gao IJMPCS(12)-a1108 [as a scalar field, and holographic dark energy].

"Von Freud Pseudotensor" > There is no such thing; The correct name is Freud Pseudotensor.

Von Neumann Algebra > see observable algebras.

Von Neumann Entropy > see entropy in quantum theory.

Von Neumann's Theorem > see representations of quantum mechanics [Stone-von Neumann].

Voronoi Complex / Polyhedron / Tiling > see voronoi tiling.

Voros Bracket / Product > see poisson brackets.

Vortex > s.a. gauge theories [vortices in condensed-matter physics]; QCD; topological defects; topology in physics.
* Idea: Another name for a global cosmic string, due to spontaneous breaking of a global symmetry; The energy density is not concentrated on a narrow tube, but diverges if integrated over all distances from the string.

Vortex Lines > see spacetime structure.

Vorticity of a Congruence of World-Lines
$ Def: If ua is the unit timelike tangent vector to the congruence, one defines the vorticity tensor and its trace as

ωab:= q[am qb]nm un ,      ω:= (\(1\over2\)ωab ωab)1/2 .

Vorticity of a Cosmological Model > see bianchi models; cmb.

VSL Theories > see varying constants [speed of light].

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