Quantum Mechanics in General Backgrounds| Quantum Mechanics in General Backgrounds |
Curved Spaces / Spacetimes > s.a. path-integral approach;
quantum states [space of states]; 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];
Perche & Neuser a2012;
> s.a. decoherence; pilot-wave theory.
@ In Schwarzschild spacetime:
Donoghue & Holstein AJP(86)sep;
Kohli a1110;
Exirifard & Karimi a2105
[from field theory in curved spacetime, and effects].
@ Other isolated objects:
de Siqueira et al ht/97 [black hole];
Gossel et al GRG(11)-a1006 [static gravitational field, scalar-particle energy levels].
@ 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 PRD(17)-a1612 [many-body, optomechanics experiment];
Großardt JPCS(17)-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 FP(17)-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];
Schwartz a2009-PhD [in post-Newtonian gravitational fields].
Quantum Gravity and Generalized Backgrounds
> s.a. non-commutative physics; quantum spacetime.
* On a lattice: We want to calculate
\(G_{\rm E}^{~}(x_2^{~},t; x_1^{~}, 0) = \int_0^t{\cal D}x(t) \exp[-S_{\rm E}^{~}/\hbar]\),
and we substitute in the action dx/dt by \([x(t_i) - x(t_{i-1})]
/\delta t\); 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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