Particles: Quantum Description |
Non-Relativistic Particle
> s.a. quantum mechanics and modified quantum mechanics;
particles; quantum systems; wigner
function.
@ General references: Vaidman PRA(13)-a1304 [the past of a quantum particle];
Dreyfus et al a1507-proc
[PER: students negotiating the boundary with classical particles];
Nisticò a1811 [alternative approach to quantization];
Das a1812 [quantifying the particle nature of a quantum state];
Kuzmichev & Kuzmichev a2007 [classicality conditions].
@ Special situations: Kuchař PRD(80) [in a Newtonian gravitational field, coordinate-independent];
Alba IJMPA(06)ht/05 [in non-inertial frames];
Louko GRG(15)-a1404 [Hamiltonian with a quantum-gravity-motivated \(p^3\) correction term];
Carlone et al a1407 [in a quantum environment of localized spins];
Lian et al AdP(18)-a1703
[particle on a hypersurface, geometric potential in Dirac quantization].
Relativistic Particle
> s.a. particle statistics; path integrals.
* Dirac quantization:
Gives p2 |ψ\(\rangle\) = 0, or
∂a∂a
ψ = 0, the Klein-Gordon equation.
* Faddeev method:
Gives x0 = t,
p0 = (pi
pi)1/2
(gauge fixing), and i ∂tψ
= H*ψ.
* Difficulty: Localizing the
particle in a region smaller than its mass gives rise to particle creation,
and thus the need for a description with a variable particle number, which
leads to quantum field theory.
@ Canonical / Dirac quantization:
Sutton PhD(67)-IJTP(07);
Benn & Tucker PLA(91);
Welling NPPS(97)gq,
CQG(97)gq,
Matschull & Welling CQG(98)gq/97 [2+1];
Wu JMP(98) [Yang-Mills background];
Hong et al MPLA(00)qp/99;
Gavrilov & Gitman CQG(00)ht;
Von Zuben JMP(00) [and localization];
Pavšič CQG(03)gq/01 [operator ordering];
Freidel et al PRD(07)ht [algebra of Dirac observables and DSR].
@ Proper-time parametrization: Cooke PR(68);
García Álvarez & Gaioli IJTP(99)ht/98 [vs hyperplane];
Gill et al JPCS(15)-a1503.
@ Path integral, Minkowski space: Ikemori PRD(89);
Gür FP(91);
Guven & Vergara PRD(91);
Tuite & Sen MPLA(03)ht-conf [closed worldlines];
Chiou CQG(13)-a1009 [timeless].
@ Path integral, decoherent histories:
Halliwell & Thorwart PRD(01)gq;
Koch & Muñoz a2012.
@ Spin-1/2 particle: Brody & Hughston PRS(99)gq/97 [in heat bath];
Alscher & Grabert JPA(99)qp [in a magnetic field];
Ghosh JMP(01)ht [Batalin-Tyutin];
Yuan et al IJTP(10) [in a magnetic field, Wigner function];
Alberto et al PLA(11)-a1102 [Dirac particle in a 3-dimensional box];
Azevedo et al AP(15)-a1506 [in an external electric field];
> s.a. quantum correlations.
@ Other spinning: Jarvis et al JPA(99)ht;
Keppeler PRL(02) [torus/semiclassical quantization];
Bastianelli et al JHEP(05) [spin-2, supersymmetric];
Kalmykov et al JPA(08) [phase space equilibrium distribution function];
Seidewitz AP(09)-a0804 [spacetime path formalism];
Nieto & Pérez-Enríquez a1102 [on a Möbius strip];
Michel CMP(15)-a1208 [conformally equivariant quantization];
Deguchi et al IJMPA(14)-a1309 [massless, twistor model];
Simulik a1409 [arbitrary mass and spin, canonical];
Horwitz & Zeilig-Hess JMP(16)-a1502 [covariant induced representations of tensors and spinors of any rank];
Bastianelli et al a1504-proc [with higher spin];
Corradini & Schubert a1604-ln [path-integral approach];
Rempel & Freidel PRD(17)-a1609 [bilocal model in terms of two entangled constituents];
Fröb & Verdaguer JCAP(17)-a1701 [one-loop quantum corrections];
Morales et al EPJC(19)-a1910 [massless, charged];
Obukhov a1912-proc [in external fields, formalism];
Kowalski-Glikman & Rosati PRD(20)-a1912 [arbitrary spin, path-integral quantization];
Horwitz a2009
[Stückelberg-Horwitz-Piron theory in general relativity];
> s.a. relativistic quantum mechanics [spin operators].
@ Related topics:
Cariñena et al JPA(90) [phase space];
Fanchi FP(94) [wave equation];
Mazur APPB(95)ht/96 [gravitating];
Ruffini gq/98 [approaches];
Razmi & Abbassi MPLA(00)gq [modified commutation relations for m = 0];
Suzuki et al ht/04 [light-front quantization];
Seidewitz JMP(06)qp/05,
qp/05-wd [spacetime path formalism; localized states];
Djama PS(07) [quantum trajectories];
Cariñena et al a0912-in [in the field of a magnetic monopole];
Stern PLA(11)-a1011 [alternative quantizations with discrete position and time];
Rusov & Vlasenko a1202-conf [and Stückelberg equation];
Katz IJMPA(19)-a1804 [worldline length operator].
> Related topics:
see 3D quantum gravity; BRST; fock space;
quantum effects [time of arrival]; uncertainty principle.
In Curved or Quantum Spacetime
> s.a. relativistic quantum mechanics; quantum
fields in curved spacetime; singularity types [as probes].
@ General references:
Kalinin gq/97 [s = 0, canonical];
Alsing et al GRG(01) [s = 0, 1/2, 1; WKB];
Gavrilov & Gitman CQG(01)ht;
Piechocki CQG(04)gq/03 [on hyperboloid];
Tagirov qp/01-conf [canonical/path integral];
Hong & Rothe AP(04)ht/03 [on Sn−1, Hamilton-Jacobi];
Obukhov et al PRD(13).
@ 3D: Cariñena et al JMP(12)-a1211 [spherical and hyperbolic spaces, curvature-dependent approach];
Arzano et al CQG(14)-a1305 [coupled to Einstein gravity, curved momentum space
and deformed algebra of creation and annihilation operators in Fock space];
Struyve GRG(21)-a2012 [Wheeler-DeWitt quantization].
@ Path integral: Cheng JMP(72);
Ferraro PRD(92);
Krtouš CQG(04)gq/00.
@ (Anti-)de Sitter space: Piechocki gq/01,
CQG(03)gq/02 [dS, different topology];
Lucietti JHEP(03)ht [AdS3];
Gazeau & Piechocki JPA(04)ht/03 [dS, coherent state];
Gazeau et al gq/05 [2D dS, methods].
@ Other specific types of spacetimes: Deser & Jackiw CMP(88) [on 2+1 conical spacetime, scattering];
Siopsis PRD(00)ht [near extreme Reissner-Nordström];
Muniz et al AP(14)-a1403 [in a rotating cosmic string spacetime];
Lienert & Tumulka a1805
[relativistic quantum theories with a fixed number of particles in FLRW spacetimes];
> s.a. particles in schwarzschild spacetime.
@ Non-commutative space:
Bigatti & Susskind PRD(00)ht/99 [plane];
Adorno et al PRD(10)-a1008 [non-relativistic];
Lu & Stern NPB(12)-a1110 [Snyder space].
@ Quantum / generalized spacetime: Naudts & Kuna JPA(01)ht/00;
Kull PLA(02);
Canarutto IJGMP(05)mp-proc ["quantum bundles"];
Santos PLA(06)qp/05 [in random spacetime, and the Schrödinger equation];
Nicolini & Niedner PRD(11)-a1011 [Hausdorff dimension of path];
Farrelly & Short PRA(14)-a1312 [single quantum particle in discrete spacetime];
> s.a. Non-Archimedean Structures.
And Quantum Field Theory
> s.a. Bosons; fermions;
fock space [number operator]; particle physics
[theories]; QED; quantum field theories.
@ Particles and localization:
Newton & Wigner RMP(49);
in Feynman 62;
Hegerfeldt PRL(85);
Buchholz et al PLB(91);
Horwitz & Usher FPL(91);
Clifton & Halvorson BJPS(01)qp/00;
Barat & Kimball PLA(03)qp/01 [save causality];
Wallace qp/01 [bosonic];
Halvorson & Clifton PhSc(02)qp/01 [support for Malament's argument];
Comtet et al JPA(05) [random environment, and graphs];
> s.a. localization.
@ Particle dynamics: Hu & Johnson qp/00-conf [Unruh effect, non-equilibrium];
Johnson & Hu qp/00-conf,
qp/00;
> s.a. quantum field theory effects in curved spacetime.
@ Related topics:
Woodard gq/98 [particle masses];
Wu et al AP(12)-a0809 [and electromagnetic squeezed vacuum];
Belokurov & Shavgulidze a1511 [masses and functional measures];
> s.a. causality; Singletons.
Other Quantum Models and Generalizations
> s.a. Landau Model; membranes [higher-dimensional];
Topological Particle Theory; twistors.
* Quantum deformed mass shell:
Defined by (2κ sinh{p0
/ 2κ})2
− pi
pi
= m2.
@ Infraparticles, particle weights: Buchholz & Porrmann; Porrmann
PhD(99)ht/00,
CMP(04)ht/02,
CMP(04)ht/02.
@ Superparticle:
Galvão & Teitelboim JMP(80) [classical];
Brink et al NPB(87);
Dur PLB(88) [BRST];
Kowalski-Glikman et al PLB(88) [spinning];
Bengtsson PRD(89);
Bergshoeff & Van Holten PLB(89);
Au & Spence MPLA(94) [covariant phase space];
Schray CQG(96)ht/94 [9+1 spacetime solution];
Nielsen & Nielsen AP(00)ht;
Hatsuda et al JHEP(09)-a0812 [4D N = 4];
Mezincescu & Townsend Sigma(11)-a1011-proc [3D N = 1];
McKeon a1209 [massless, canonical analysis];
Mezincescu et al JPA(14);
Bergshoeff et al PRD(14)-a1406 [non-relativistic, in a curved background].
@ Superparticle, covariant:
Lindström et al JMP(90);
Chesterman JHEP(04)ht/02 [10D].
@ And quantum gravity: 't Hooft CQG(96)gq [2+1, and spacetime discreteness];
Dalvit & Mazzitelli PRD(97)ht [corrected motion].
@ Quantum deformed: Lukierski et al AP(95);
Sánchez et al IJMPA(08)-a0705 [with electromagnetic fields];
> s.a. deformation quantization.
@ Related topics: Gudder IJTP(86) [in terms of graphs];
Rogers NPPS(00)ht,
CQG(00)ht [topological, BRST quantization];
Balasubramanian & Larsen NPB(97) [branes];
Christian mp/04 [representations over adele rings];
Stoilov CEJP(07)ht [fermions as U(1) instantons];
Wetterich a0904,
AP(10),
IJTP(12)-a1003 [from classical probabilities],
PLA(12)-a0911
[Zwitters, common classical statistical mechanics setting for classical and quantum particles].
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