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).

* 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.

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