Stochastic Quantization| Stochastic Quantization |
In General
* Idea: Quantum mechanics or
quantum field theory is formulated as an equilibrium state of a statistical
system coupled to a thermal reservoir in Euclidean space (see, e.g., the
Fokker-Planck equation); This can be considered as an independent approach
to quantum theory, or as a tool to evaluate (Euclidean) path integrals, with
the same physical interpretation; It is used mostly for gauge field theories.
* Remark: The real time t
of quantum theory cannot be used as the evolution parameter of the stochastic
process, since then one does not get the Schrödinger equation.
References
> s.a. modified quantum mechanics [stochastic extension]; pilot-wave theory.
@ Proposal: Nelson PR(66);
Parisi & Wu SS(81);
Altaisky ht/05-conf [multiscale version, wavelet-based].
@ General: Yasue IJTP(79) [rev];
Kracklauer PRD(74);
Ali RNC(85);
Mielnik & Tengstrand IJTP(80) [criticism];
Guerra & Marra PRD(83) [and operator algebra];
Damgaard & Hüffel PRP(87),
ed-88;
Klauder in(87);
Parisi 88; Haba 99
[r Maassen van den Brink qp/02];
Masujima 00;
Derakhshani a1804-PhD [without an ad hoc quantization].
@ Related topics:
de la Peña-Auerbach & Cetto PRD(71) [self-interaction],
NCB(72) [diffusion coefficient];
Smolin PLA(86) [quantum diffusion constant and inertial mass];
Pugnetti NPB(88) [renormalization group];
Iengo & Pugnetti NPB(88) [non-markovian regularization],
NPB(88) [critical exponents];
Wang PRA(88) [role of interference];
Fliess qp/06 [quantum fluctuations];
Mansi et al PLB(10) [and AdS/cft].
@ Quantum mechanics and stochastic mechanics:
Carlen & Loffredo PLA(89) [multiply connected apaces];
Garbaczewski PLA(90),
PLA(90);
Schulz AdP(09)-a0807 [and Bell's inequalities].
@ Quantum mechanics from stochastic metric fluctuations:
Bergia et al PLA(89);
Calogero PLA(97).
Variations
* Stochastic variational method:
A reformulation of Nelson's stochastic quantization method from the point of view
of a variation principle.
@ General references: Beck ht/03-proc [chaotic quantization and the standard model of particle physics];
Kazinski a0704
[deformation and relativistic diffusion equation];
Hüffel IJBC(08)-a0710-conf [with non-linear Brownian motion as underlying stochastic process];
Kobayashi & Yamanaka PLA(11)-a1007 [extension to thermo field dynamics];
Kuipers a2101,
a2103 [on Lorentzian manifolds].
@ Stochastic variational method:
Yasue JFA(81);
Koide & Kodama PTEP(15)-a1306 [complex Klein-Gordon field];
Koide et al a1406 [electromagnetic field];
Yang a2102 [new variational principle, based on information measures].
Examples, Specific Theories > s.a. boundaries;
semiclassical general relativity [stochastic].
@ Quantum mechanical systems:
Durran et al JMP(08) [atomic elliptic states];
Nicolis a1405 [1D particle, and supersymmetry].
@ Ising model:
Bérard & Grandati IJTP(99).
@ Fermions: Guerra & Marra PRD(84);
Horsley & Schoenmaker PRD(85);
Garbaczewski FdP(90) [neutral spin-1/2];
Efremov IJTP(19)-a1804 [massive].
@ Electrodynamics: Claverie & Diner IJQC(78);
Davidson JMP(81);
Puthoff PRA(89);
Hüffel & Kelnhofer PLB(04)ht/03 [= path integral].
@ Gauge theory: Hüffel & Kelnhofer AP(98)ht [Yang-Mills];
Masujima 00;
Zwanziger PRD(03)ht/02;
Kapoor MPLA(19)-a1811 [axial vector].
@ Quantum gravity: Prugovečki 84;
Klauder in(86);
Rumpf in(86);
Miller JMP(99) [1+1];
Moffat a1402
[singularities in gravitational collapse, and grey holes];
Gokler a2003 [and estimation theory];
> s.a. approaches to quantum gravity;
hořava gravity.
@ Linearized gravity: Davidson JMP(82)qp/01.
@ Scalar fields: Menezes & Svaiter PhyA(07)ht/05
[λφ4 theory];
Menezes & Svaiter JPA(07)-a0706 [in Einstein and Rindler spaces];
de Aguiar et al CQG(09) [in de Sitter space];
de Aguiar et al a0908 [at finite temperature];
dos Reis et al PLB(19)-a1804
[self-interacting non-minimal massive scalar field in curved spacetime].
@ Supersymmetric theories: Farajollahi & Luckock gq/04/IJTGN [locally supersymmetric];
Baulieu PLB(19)-a1812 [stochastic quantization].
@ Other examples:
Garbaczewski JPA(87) [Fermi oscillator];
Lim & Muniandy PLA(04) [non-local fields];
Hotta et al ht/04 [Born-Infeld theory];
Haas IJTP(05) [time-dependent oscillator];
Bhattacharjee & Gangopadhyay cm/05 [non-equilibrium statistical mechanics];
Menezes & Svaiter JMP(06)ht [topological field theory];
Scarfone JSM(07)cm [interacting particle systems];
Menezes & Svaiter JMP(08)-a0807 [systems with complex-valued path integral weights];
Dijkgraaf et al NPB(09) [relating field theories];
> s.a. casimir force.
main page
– abbreviations
– journals – comments
– other sites – acknowledgements
send feedback and suggestions to bombelli at olemiss.edu – modified 4 mar 2021