Modified Formalisms for Quantum Theory| Modified Formalisms for Quantum Theory |
In General > s.a. foundations; path
integrals; quantum theory on generalized backgrounds [including curved spaces].
@ General references: Bastin ed-70;
Jordan in(72);
Mielnik CMP(74);
Wignall FP(88);
Hoekzema 93;
Budnik ht/94;
Beretta MPLA(05) [constraints from consistency with thermodynamics];
Asorey et al JPA(13)-a1301 [with rapidly changing boundary conditions].
@ Modified postulates: Sudbery SHPMP(02)qp/00,
qp/00-conf [re quantum jumps];
Svozil qp/00 [re probabilities].
@ Non-Hamiltonian: Bolivar PRA(98);
Tarasov qp/01,
PLA(01)qp/03;
Gitman & Kupriyanov EPJC(07)ht/06;
Vol PRA(06)qp/05;
Sergi JCP(07)qp/05;
> s.a. Open Systems.
@ Generalized measures: Sorkin MPLA(94)gq [quantum measure];
Chryssomalakos & Durdevich MPLA(04)qp/03;
> s.a. measure theory.
@ Time-symmetric theory:
Aharonov et al PR(64);
Vaidman a0706-en;
Aharonov et al PT(10)nov;
Bopp FP(17)-a1604 [and macroscopic physics];
Kastner a1607;
Leifer & Pusey PRS(17)-a1607
[impossibility of a non-retrocausal time-symmetric ontology].
@ Non-reversible, semigroup:
Petrosky & Prigogine PhyA(88),
PLA(93) [for density matrices];
Castagnino & Laura PRA(97)qp/96;
Bohm et al IJTP(03)ht/99,
ht/99,
PLA(00)ht/99,
ht/99-proc [Gamow vectors].
@ Pre-quantum mechanics: Adler & Millard NPB(96)ht/95;
Durdevich qp/99 [C*-algebra];
Soucek qp/01;
Khrennikov qp/03 [no "no-go"].
@ Event-enhanced:
Blanchard & Jadczyk PLA(95),
AdP(95)ht/94,
qp/95,
RPMP(95)qp [and measurement],
FP(96)qp [relativistic].
@ Generalized frameworks: Fischbach et al PRL(91) [different \(\hbar\)];
Aerts & Gabora Kyb(05)qp/04,
Kyb(05)qp/04 [state-context-property theory];
Hardy & Wootters FP(12)-a1005
[theories more holistic than quantum theory, bilocally tomographic];
Kisil IJTP(12)-a1005
[general representations of the Heisenberg group, including classical and quantum mechanics];
Moldoveanu a1311 [hyperbolic quantum mechanics, non-viability];
Brody JPA(14) [biorthogonal quantum mechanics];
Gould & Afshordi FP(15)-a1407 ["real ensemble" non-local description];
Krause & Arenhart a1510 [based on non-reflexive logic];
Gogioso a1703 [bestiary of exotic examples];
Thas a1712 [over general division rings with involution];
Bisio & Perinotti PRS(19)-a1905 [higher-order quantum theory];
Cassa a2103 [realistic, deterministic extension].
@ Other modifications:
Zambrini PRA(87) [euclidean];
Adler & Horwitz JMP(96)ht;
Fivel PRA(94) [tests];
Petrov qp/97;
Baugh et al FP(03)ht [ultraquantum theory];
Fivel qp/03 [metaplectic];
Kitada qp/04 [??];
Khrennikov FPL(05) [from statistical field theory];
Aharonov et al PRA(09)-a0712 [multiple-time states];
Ghirardi & Romano PRL(13)-a1301,
FP(13)-a1301
[extension of quantum theory, predictively inequivalent ontological model];
Sellier & Kapanova a1704 [signed quantum mechanics, and the H atom];
Strumia a1709 [with indefinite norm];
Grassi & Mariño Sigma(19)-a1806 [exactly solvable deformation].
> Related topics:
see Adelic Structures; categories in physics;
clifford algebra; differential geometry;
fractional calculus; Galois Field [finite
field]; Groupoids; Hypercomplex Numbers;
Modal Quantum Theory; Non-Associative
Algebras; non-standard analysis; Octonions;
p-Adic Structures; quaternions;
Topos.
Different Hilbert Spaces
> s.a. Banach Space [use of \(\mathbb{KS}^2\)].
* Idea:
Quantum theories may be formulated in real, complex or quaternionic Hilbert
spaces only, but there are physical reasons for ruling out real Hilbert spaces
that rely on Heisenberg's principle (results cited by Oppio & Moretti).
@ General references:
Namiki & Pascazio PLA(93),
PRP(93) [many];
Myrheim qp/99 [real];
Znojil a0910-conf;
Oppio & Moretti RVMP(17)-a1611 [real Hilbert space].
@ Evolving Hilbert spaces: Mostafazadeh PLA(04)qp/03;
Artacho & O'Regan PRB(17)-a1608.
@ Alternatives to Hilbert spaces:
Anastopoulos FP(01)qp/00 [probabilities and phases];
Niestegge FP(14)-a1402 [ordered Banach spaces, and absence of third-order interference];
Zohar JPA(17)-a1607 [stators, half states and half operators].
main page
– abbreviations
– journals – comments
– other sites – acknowledgements
send feedback and suggestions to bombelli at olemiss.edu – modified 17 mar 2021