Particles: Quantum Description  

Non-Relativistic Particle > s.a. quantum mechanics and modified quantum mechanics; particles.
@ 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].
@ 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 p3 correction term]; Carlone et al a1407 [in a quantum environment of localized spins]; Lian et al a1703 [particle on a hypersurface, geometric potential in Dirac quantization].

Relativistic Particle
* Dirac quantization: Gives p2 |ψ\(\rangle\) = 0, or ∂aaψ = 0, the Klein-Gordon equation.
* Faddeev method: Gives x0 = t, p0 = (pipi)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.
@ 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 a1609 [bilocal model in terms of two entangled constituents]; Fröb & Verdaguer a1701 [one-loop quantum corrections]; > 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].
> Related topics: see 3D quantum gravity; BRST; fock space; particle statistics; path integrals; quantum effects [time of arrival].

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].
@ 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]; > 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})2pipi = 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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