Relativistic Quantum Mechanics |
Quantum Mechanics and Special Relativity
> s.a. causality in quantum theory; formalism;
history of quantum theory; quantum theory in curved spaces.
* 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 = β (m2 + p2)1/2 + V(r) .
@ Reviews, books: Bjorken & Drell 64;
Bethe & Jackiw 68;
Fanchi AJP(81)sep [review and critique];
Landau 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];
Ohlsson 11;
Horwitz 15;
Padmanabhan EPJC(18)-a1712 [and quantum field theory];
Pauchy Hwang & Wu 18.
@ Quantum mechanics and Poincaré invariance:
Dieks & Nienhuis AJP(90)jul;
Cohen & Hiley FP(96);
Berg qp/98 [and measurement];
Percival PLA(98)qp,
qp/99 [measurement];
Stefanovich FP(02);
Stuckey et al PE-qp/05 ["Relational Blockworld"];
Polyzou et al FBS(11)-a1008-conf [rev];
Seevinck a1010-conf [compatibility];
Blackman a1310 [action at a distance and causality];
Mamone-Capria JFAP-a1704 [historical];
Butterfield a1710 [peaceful coexistence?].
@ General references: Dirac RMP(49);
Dutheil & Lochak AFLB(91);
Caban & Rembieliński PRA(99)qp/98 [preferred frame];
Treumann PS(02);
Semenov PhD(02)qp [phase-space formulation];
Gill & Zachary JMP(02) [Feynman's operator calculus];
Mangiarotti & Sardanashvily JMP(07)qp [different reference frames];
Krotov a0804;
Kryukov JMP(08),
JMP(10)-a1005 [unifying framework];
Krotov a0903 [wave function];
Kauffmann a0909 [for solitary non-zero-mass particle];
Kastner a1002
[transactions and Tumulka's "flash ontology"];
Cabrera et al a1107 [in Hilbert space];
Bateson JPCS(12) [causal-net approach];
Simulik a1509 [canonical];
Tsai & Poirier JPCS(16)-a1605 [quantum wavepackets in the trajectory-based formulation];
Leegwater a1811
[against relativistic, unitary, single-outcome quantum mechanics];
Fröhlich a1912-in [operator-algebraic framework].
@ And time: Shapiro JPA(08)-a0802 [proper-time evolution equation];
Bauer a1605 [time operator].
@ Realism and Lorentz invariance:
Comborieu & Vigier PLA(93) [compatible];
Marchildon PhyE(10)-a0902-conf;
> s.a. realism.
@ Hidden-variable versions: Horton & Dewdney JPA(01)qp [non-local];
Nikolić a1010 [almost local],
a1205-ch
[based on many-time wave functions and the spacetime probabilistic interpretation].
@ Interpretation: Cosgrove gq/96 [single-particle];
Nikolić IJMPA(07)qp/06 [probabilities and spacetime foliations];
Gorobey et al a1012 [probabilistic];
> s.a. foundations.
@ EPR correlations, 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;
Albert & Galchen SA(09)mar [and non-locality];
Caban et al PRA(09)-a0904 [strange behavior].
@ Classical limit: Silenko a0910-conf;
Silenko PPNL(13)-a1302 [in the Foldy-Wouthuysen representation].
@ Related topics:
Greenberger PRL(01) [non-relativistic limit];
Rembieliński & Smoliński EPL(09)-a0910 [test for existence of preferred frame];
Gisin a1002
["true becoming" and the Free Will Theorem];
Falciano et al FP(10) [geometric formulation];
Yuan et al NPJQI(15)-a1412 [entanglement and the benefits of ctc's without violating causality];
> s.a. Bethe-Salpeter Equation; Correspondence
Principle; Galilean Group; Simultaneity;
uncertainty principle.
Systems and Phenomenology > s.a. composite
systems [many-particle systems]; entanglement phenomenology;
path integrals; types of states.
@ Multiple particles:
Mattes & Sorg JPA(99) [two];
Beck & Sorg FP(07) [2- and 3-particle systems];
Lienert et al JPCS(17)-a1702 [N particles, multi-time];
Giachetti & Sorace AP(19)-a1810 [two interacting particles].
@ Types of systems:
Kim & Noz qp/03-conf [oscillator];
Nagiyev & Guliyeva PLA(09) [particle in a homogeneous external field];
Alba et al JPA(13)-a1107 [two-level atom];
Kim a1112-proc [boosted hydrogen atom];
Al-Hashimi & Shalaby a1406 [δ-function potential];
Calmet & Dunningham PRA(17)-a1703 [qubit, transformation properties and entanglement];
Polyzou PRC(19)-a1809 [particles of arbitrary spin].
@ Phenomenology: Khachidze & Khelashvili AJP(06)jul [Coulomb problem, additional symmetries and conserved quantities];
Beck et al a0704 [positronium ground state];
Azfar 15 [scattering and particle physics];
Kamuntavičius a1302 [relativistic corrections to energy spectra];
Alavi & Giunti EPL(15)-a1412,
Urbanowski a1504 [decay law for relativistic particles];
> s.a. molecular physics; oscillators.
Variations and Related Topics
> s.a. fractals [paths]; hidden-variable
theories; pilot-wave theory; tachyons;
tunneling; wave-function collapse.
@ Salpeter equation: Hall et al IJMPA(03)ht/02 [discrete spectra].
@ Parametrized relativistic quantum theory:
Fanchi FP(01) [implements non-locality].
@ Causal quantum theory: Roy & Singh MPLA(95)hp/94;
Kent PRA(05)qp/02.
@ In different reference frames: Mashhoon LNP(06)ht/05 [accelerated frames];
Mangiarotti & Sardanashvily JMP(07) [formalism].
@ Semi-relativistic quantum mechanics:
Hall & Lucha JPA(05) [eigenvalues];
Hall JPA(06) [non-local potentials];
Rosenau & Schuss PLA(11)-a1007.
@ In non-inertial frames: Alba IJMPA(06);
Klink & Wickramasekara AP(14)-a1303 [and violations of the equivalence principle].
@ 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-conf;
Hartle IJTP(06)gq/05-in;
Corbett & Durt qp/05;
Olson & Dowling a0708 [unitarity, realism];
Wallace & Timpson BJPS(10)-a0906;
Herczeg & Waldron PLB(18)-a1709 [generally covariant quantum mechanics on 'phase spacetime'];
> s.a. histories quantum mechanics.
@ Relativistic spin operators: Bauke et al NJP(14)-a1303;
Choi & Cho a1410;
Zou et al a2003 [Foldy-Wouthuysen representation];
Taillebois & Avelar a2008 [intrinsic];
> s.a. quantum particles.
@ Other topics: García Álvarez & Gaioli IJTP(97)ht/98 [based on de Sitter group];
Habara et al IJMPA(06)ht/05 [supersymmetric, relativistic];
Fournais & Sørensen CPDE-a0811 [pseudorelativistic model of atoms];
Bender & Mannheim PRD(11)-a1107,
Beygi et al PRA(19)-a1904 [PT symmetric];
Dvoeglazov proc(15)-a1511 [tensor fields, notoph and photon, and gravitational field equations].
> Related topics:
see modified quantum theory [non-hermitian]; non-linear quantum mechanics;
phase-space formulation; quantum effects [time of arrival, state
diffusion]; time in quantum theory [quantum mechanics without predefined time].
main page
– abbreviations
– journals – comments
– other sites – acknowledgements
send feedback and suggestions to bombelli at olemiss.edu – modified 21 aug 2020