Quantum Particle Models  

Quantization of Non-Relativistic Particle > s.a. quantum mechanics.
@ References: Kuchar PRD(80) [in Newtonian gravitational field, coordinate-independent]; Alba IJMPA(06)ht/05 [in non-inertial frames].

Quantization of Relativistic Particle
* Dirac quantization: Gives p2 | = 0, or aa = 0, the Klein-Gordon equation.
* Faddeev method: Gives x0 = t, p0 = (pipi)1/2 (gauge fixing), and i t = H*.
* 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: 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]; García Álvarez & Gaioli IJTP(99)ht/98 [hyperplane vs ]; Hong et al MPLA(00)qp/99; Gavrilov & Gitman CQG(00)ht; Von Zuben JMP(00) [and localization]; Pavsic CQG(03)gq/01 [operator ordering]; Freidel et al PRD(07)ht [algebra of Dirac observables and DSR]; Sutton IJTP(07)-PhD.
@ Path integral, Minkowski: Ikemori PRD(89); Gür FP(91); Guven & Vergara PRD(91); Tuite & Sen MPLA(03)ht-in [closed worldlines].
@ Path integral, decoherent histories: Halliwell & Thorwart PRD(01)gq.
@ Spin-1/2: Brody & Hughston PRS(99)gq/97 [in heat bath]; Alscher & Grabert JPA(99)qp [in B field]; Ghosh JMP(01)ht [Batalin-Tyutin].
@ 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 equlibrium distribution function]; Seidewitz AP(09)-a0804 [spacetime path formalism].
@ Related topics: Cooke PR(68) [proper time parametrization]; 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 [spacetime path formalism; localized states]; Djama PS(07) [quantum trajectories].
> 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; types of singularities [as probes].
@ General references: Deser & Jackiw CMP(88) [on 2+1 conical spacetime, scattering]; Kalinin gq/97 [s = 0, canonical]; Siopsis PRD(00)ht [near extreme Reissner-Nordström]; 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-in [canonical/path integral]; Hong & Rothe ht/03 [on Sn–1, Hamilton-Jacobi]; Lucietti JHEP(03)ht [on AdS3].
@ Path integral: Cheng JMP(72); Ferraro PRD(92); Krtous CQG(04)gq/00.
@ de Sitter space: Piechocki gq/01, CQG(03)gq/02 [different topology]; Gazeau & Piechocki JPA(04)ht/03 [coherent state]; Gazeau et al gq/05 [2D, methods].
@ Quantum / generalized spacetime: Bigatti & Susskind PRD(00)ht/99 [non-commutative plane]; Naudts & Kuna JPA(01)ht/00; Kull PLA(02); Dimitrijevic et al FU(04)ht [non-archimedean]; Canarutto mp/05-in ["quantum bundles"]; Santos PLA(06)qp/05 [in random spacetime, and the Schrödinger equation]; > s.a. non-commutative physics.

And Quantum Field Theory > s.a. causality; fock space [number operator]; particle physics [theories]; QED; quantum field theories.
@ Particles and localization in quantum field theory: 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. locality.
@ Particle dynamics: Hu & Johnson qp/00-in [Unruh effect, non-equilibrium]; Johnson & Hu qp/00-in, qp/00; > s.a. quantum field theory effects in curved spacetime.
@ Related topics: Woodard gq/98 [particle masses]; Wu et al a0809 [and electromagnetic squeezed vacuum]; > s.a. Singletons.

Other Quantum Models and Generalizations > s.a. membranes [higher-dimensional]; Topological Particle Theory; twistors.
* Quantum deformed mass shell: Defined by (2 sinh{p0 / 2})2 – pipi = m2.
@ Infraparticles, particle weights: Buchholz & Porrmann; Porrmann ht/00-PhD, 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; Ivanov a0705-in [superextension of Landau model on a plane]; Hatsuda et al a0812 [4D N = 4].
@ 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, a0911 [common classical statistical mechanics setting for classical and quantum particles].

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