Quantum Mechanics and Special Relativity > s.a. Bethe-Salpeter
Equation; causality; quantum
effects, formalism, types of
states.
* Hardy's theorem: The
hidden variables of any realistic theory of quantum measurement, whose predictions
agree with ordinary quantum theory, must have
a preferred Lorentz frame.
* Shimony's peaceful coexistence:
Bell's
theorem suggests that quantum physics is fundamentally non-local; Yet, entanglement
cannot be used for practical non-local signalling; This amounts to
a peculiar "conspiracy" in the laws of physics.
* Semi-relativistic form: The wave equation is the Salpeter equation,
and the Hamiltonian is of the form
H =
(m2
+ p2)1/2 + V(r)
.
@ Reviews, books: Bjorken & Drell 64; Bethe & Jackiw 68; Fanchi AJP(81)
[review and critique];
RLandau
96;
Strange
98
[including
condensed matter]; Capri 02; Strocchi FP(04)
[and quantum field theory]; Fanchi FP(05)
[introduction]; Pilkuhn 05; De Sanctis a0708 [and
Dirac equation].
@ Quantum mechanics and Poincaré invariance: Dieks & Nienhuis AJP(90);
Cohen & Hiley
FP(96);
Berg
qp/98 [and
measurement]; Percival PLA(98)qp,
qp/99 [measurement];
Stefanovich FP(02);
Kim & Noz
qp/03-in
[oscillator]; Stuckey et al qp/05/PE
["Relational
Blockworld"].
@ General references: Dirac RMP(49);
Dutheil & Lochak AFLB(91);
Caban & Rembielinski PRA(99)qp/98 [preferred
frame]; Mattes & Sorg JPA(99)
[two particles]; Treumann PS(02);
Semenov qp/02-PhD
[phase space formulation]; Gill & Zachary
JMP(02) [Feynman's
operator calculus]; Mangiarotti & Sardanashvily JMP(07)qp [different
reference frames]; Shapiro JPA-a0802 [proper-time
evolution equation]; Krotov a0804.
@ Phenomenology:
Khachidze & Khelashvili AJP(06)
[Coulomb problem, additional
symmetries
and
conserved quantities]; Beck et al a0704 [positronium
ground state]; > s.a. oscillators.
@ Realism and Lorentz invariance:
Comborieu & Vigier PLA(93)
[Lorentz invariance and realism
ok]; > s.a. realism.
@ Interpretation: Cosgrove gq/96 [single-particle];
Horton & Dewdney
qp/01 [non-local
hidden variables]; Nikolic IJMPA(07)qp/06
[probabilities
and spacetime foliations]; > s.a. quantum foundations.
@ Semi-relativistic quantum mechanics: Hall & Lucha JPA(05)
[eigenvalues]; Hall JPA(06)
[non-local potentials].
@ EPR paradox: Ghose & Home PRA(91); Zbinden
et al PRA(01);
Tiwari PRA(02)qp/01;
Kim & Son PRA(05)qp/04 [Lorentz-invariant];
O'Hara qp/06.
@ Related topics: Greenberger PRL(01)
[non-relativistic limit]; Beck & Sorg FP(07)
[2- and 3-particle systems]: > s.a. Galilean
Group.
Variations and Related Topics > s.a. fractals [paths]; hidden
variables; quantum effects [arrival time];
tachyons.
@ Salpeter equation: Hall et al IJMPA(03)ht/02 [discrete
spectra].
@ Parametrized relativistic qquantum theory: Fanchi FP(01)
[implements non-locality].
@ Causal: Roy & Singh MPLA(95)hp/94;
Kent PRA(05)qp/02.
@ In different reference frames: Mashhoon ht/05-in
[accelerated frames]; Mangiarotti & Sardanashvily JMP(07)
[formalism].
@ Spacetime versions: Hartle in(98)gq/97,
in(98)gq [generalized
quantum mechanics]; Rudolph PRA(99)mp/98;
Anastopoulos JMP(01)qp/00,
FP(01)qp/00 [histories-based];
Reisenberger & Rovelli PRD(02)gq/01;
Marolf & Rovelli
PRD(02)gq [measurement];
Krasnoholovets qp/02-in;
Hartle gq/05-in;
Corbett
& Durt qp/05;
Alba
IJMPA(06)
[non-inertial frames]; Olson & Dowling a0708 [unitarity,
realism]; > s.a. histories
quantum mechanics.
@ Other topics: García Álvarez & Gaioli IJTP(97)ht/98 [based
on de Sitter group]; Habara
et al IJMPA(06)ht/05 [supersymmetric,
relativistic]; Elze a0704-in
[non-linear, relativistic]; > s.a. phase space
formulation.
And Curved Spaces, Covariance, and Gravity > s.a. causality
violations; newton-cartan;
quantum spacetime; theta; uncertainty.
* 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).
@ In curved spacetime: Donoghue & Holstein AJP(86)
[Schwarzschild]; 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], gq/00 [FRW
spacetime]; de Siqueira et al ht/97 [black
hole]; Moreira PRA(98)ht/97,
PRA(98)ht/97 [conical
singularity]; Mensky TMP(98)gq/97 [accelerated
observers, Unruh effect]; 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]; Grain & Barrau a0705 [semiclassical
propagator]; Bakke et al JPA(08)
[EPR correlations, cosmic string background]; > s.a. decoherence, pilot
wave.
@ 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-in;
Minic & Tze PRD(03)ht,
PLB(04)ht/03;
Poulin IJTP(06)qp/05 [relational];
Olson & Dowling qp/07 [information
and measurement]; Aalok IJTP(07)qp,
a0805 [background-independent];
Kopf & Paschke JMP(07)
[non-commutative configuration spaces].
@ And quantum gravity: Bertolami PLA(91)
[corrections]; Adler NPB(94)ht/93,
& Wu PRD(94),
et al JMP(94)
[non-commutative coordinates]; Antonsen PRD(97)
[Wigner functions]; Hartle IJMPA(01)
[without background causal structure]; Isham qp/02;
Balasubramanian et al gq/02-in
[and holography]; Baez qp/04 [category
language]; Hartle gq/06-in
[generalized
quantum mechanics].
@ Related models and topics: Mondragon et al PRD(07)-a0705 [discrete,
periodic time and
space model for general relativistic quantum mechanics].
Main page – Abbreviations – Journals – Comments – Other
sites – Acknowledgements
Send feedback and suggestions to bombelli at olemiss.edu – Modified
21 jun 2008