Quantum Mechanics in General Backgrounds  

Curved Spaces / Spacetimes > s.a. path-integral approach; quantum systems [on group manifolds].
* Remark: In curved spacetime there is no momentum representation because in that case the conjugate variables would not commute and could not be represented by derivative operators.
@ Curved configuration space: Argyres et al JPA(89) [2D, negative curvature]; Foerster et al PLA(94) [as constrained system]; Tagirov IJTP(03)gq/02; Milatovic JGP(06) [separation properties]; Moschella & Schaeffer CQG(07)-a0709 [constant negative curvature]; Morchio & Strocchi LMP(07); Olpak MS-a1010; Cariñena et al JMP(11)-a1201 [on spherical and hyperbolic spaces]; Bracken Chaos(14)-a1406, JMP(14)-a1407 [on a manifold of constant curvature, using Noether symmetries]; Nakamura a1412 [operatorial quantization formalism].
@ In curved spacetime: Audretsch & de Sabbata ed-90; Yamada & Takagi PTP(91), PTP(91); Molzahn et al AP(92); Tagirov TMP(96) [spinning non-relativistic particle], G&C(99)gq/98 [canonical]; Moreira PRA(98)ht/97, PRA(98)ht/97 [conical singularity]; Kerner JMP(99) [non-associative structure]; Vitolo LMP(00) [fiber bundle formalism]; Kleinert qp/00; Alsing et al GRG(01) [spin-0, 1/2, 1, WKB]; Yurtsever & Hockney CQG(05)gq/04 [beyond Cauchy horizons]; Francis gq/06 [connection between Hilbert spaces at different points]; Grain & Barrau PRD(07)-a0705 [semiclassical propagator]; Bakke et al JPA(08) [EPR correlations, cosmic-string background]; > s.a. decoherence; pilot-wave theory.
@ Around isolated objects: Donoghue & Holstein AJP(86)sep [Schwarzschild spacetime]; de Siqueira et al ht/97 [black hole]; Gossel et al GRG(11)-a1006 [static gravitational field, scalar-particle energy levels]; Kohli a1110 [Schwarzschild spacetime].
@ Cosmological spacetimes: Tagirov gq/00 [FLRW spacetime]; Lev a0807 [two free particles in de Sitter space, and gravity]; Ghosh & Mignemi IJTP(11)-a0911 [in de Sitter space, extended uncertainty principle].
@ Other models and related topics: Mondragon et al PRD(07)-a0705 [discrete, periodic time and space model for general relativistic quantum mechanics]; Ord AP(09) [in 2D spacetime, and meaning of the wave function]; Kowalski & Rembieliński AP(13) [on a cone]; > s.a. generalized quantum mechanics.
@ Schrödinger-Newton equation: Helou et al a1612 [many-body, optomechanics experiment]; Großardt a1702 [tests]; > s.a. quantum gravity [alternatives].
> Related topics: see causality violations; newton-cartan theory; theta sectors; modified uncertainty relations; rindler space [hydrogen atom].

Quantum Mechanics and Gravity / Covariance > s.a. reference frames [accelerated observers].
@ With gravity term: Marciak-Kozlowska & Kozlowski qp/04, qp/04 [and pilot waves]; Adler JPA(07)qp/06; > s.a. wave-function collapse.
@ And general relativity, covariance: Mashhoon FP(86); Ho ht/95; Anandan MPLA(02)qp [(non-)locality]; Wawrzycki mp/03-conf; Minic & Tze PRD(03)ht, PLB(04)ht/03; Poulin IJTP(06)qp/05 [relational]; Olson & Dowling qp/07 [information and measurement]; Khrennikov a1704 [present situation].
@ Background-independent theory: Aalok IJTP(07)qp, a0805, IJTP(09); Rovelli a1108 [Hamilton function, classical limit].
@ Related topics: Oeckl ATMP(08)ht/05 [general-boundary formulation].

Quantum Gravity and Generalized Backgrounds > s.a. non-commutative physics; quantum spacetime.
* On a lattice: We want to calculate GE(x2, t; x1, 0) = \(\int_0^t\cal D\)x(t) exp[–SE/\(\hbar\)], and we substitute in the action dx/dt by [x(ti) – x(ti–1)] / δt; One then uses the Monte Carlo method to integrate over random paths.
@ And quantum gravity: Bertolami PLA(91) [corrections]; Antonsen PRD(97) [Wigner functions]; Hartle IJMPA(01) [without background causal structure]; Isham qp/02; Balasubramanian et al gq/02-proc [and holography]; Baez qp/04 [category language]; Hartle in(07)gq/06 [generalized quantum mechanics]; Kauffman & Lomonaco a1105 [quantizing algebraic, combinatorial and topological structures], Lomonaco & Kauffman SPIE(11)-a1105 [quantizing knots, graphs, groups, categories, ...].
@ Discrete time: Bender et al PRD(05), PRD(86), PRD(87); Khorrami AP(95), AP(96); Date CQG(03)gq/02.
@ Discrete spacetime: Gudder FP(88); Lorente in(97)qp/04; Piazza AIP(06)ht/05 [localized subsystems in Hilbert space]; Koehler qp/06; Odake & Sasaki PTP(10)-a0902 [correspondence with regular Schrödinger equation, Crum's theorem]; Bhatia & Swami IJTP(11)-a1011 [on a lattice]; > s.a. quantum mechanics in phase space.
@ Quantum mechanics in non-commutative spacetime: Adler NPB(94)ht/93, & Wu PRD(94), et al JMP(94) [generalized quantum dynamics]; Balachandran et al JHEP(04)ht [Moyal plane], JHEP(04)ht [cylinder]; Vaquera-Araujo & Lucio mp/05 [plane]; Calmet & Selvaggi PRD(06)ht; Kopf & Paschke JMP(07) [non-commutative configuration spaces]; Wachter qp/07, qp/07, qp/07; Noui PRD(08)-a0807.
@ Other backgrounds: Hübschmann et al CMP(09) [on a stratified space]; Vourdas JMP(11) [on \(\mathbb Q\)/\(\mathbb Z\)]; Calcagni et al JMP(12)-a1207 [fractional spacetime].

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