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].
@ Proposal: Nelson PR(66); Parisi & Wu SS(81); Altaisky ht/05-in [multiscale version, wavelet-based].
@ General: Kracklauer PRD(74); Ali RNC(85); Mielnik & Tengstrand IJTP(80) [criticism]; Guerra & Marra PRD(83) [and operator algebra]; Damgaard & Hüffel PRP(87), ed-87; Klauder in(87); Parisi 88; Haba 99 [r Maassen van den Brink qp/02]; Masujima 00.
@ 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].
@ Quantum mechanics and stochastic mechanics: Carlen & Loffredo PLA(89) [multiply connected apaces]; Garbaczewski PLA(90), PLA(90); Schulz a0807 [and Bell's inequalities].
@ Quantum mechanics from stochastic metric fluctuations: Bergia et al PLA(89); Calogero PLA(97).

Variations
@ References: Beck ht/03-in [chaotic quantization and standard model]; Kazinski a0704 [deformation and relativistic diffusion equation]; Hüffel a0710-in [with non-linear Brownian motion as underlying stochastic process].

For Specific Theories > s.a. boundaries in field theory; semiclassical general relativity [stochastic].
@ Quantum mechanical systems: Durran et al JMP(08) [atomic elliptic states].
@ Ising model: Bérard & Grandati IJTP(99).
@ Fermions: Guerra & Marra PRD(84); Horsley & Schoenmaker PRD(85); Garbaczewski FdP(90) [neutral spin-1/2].
@ 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.
@ Quantum gravity: Prugovecki 84; Klauder in(86); Rumpf in(86); Miller JMP(99) [1+1]; > s.a. approaches to quantum gravity.
@ Linearized gravity: Davidson JMP(82)qp/01.
@ Scalar fields: Menezes & Svaiter PhyA(07)ht/05 [⁴ theory]; Menezes & Svaiter JPA(07)-a0706 [in Einstein and Rindler spaces].
@ Other theories: Garbaczewski JPA(87) [Fermi oscillator]; Lim & Muniandy PLA(04) [non-local fields]; Farajollahi & Luckock gq/04/IJTGN [locally supersymmetric]; Hotta et al ht/04 [Born-Infeld theory]; Haas IJTP(05) [t-dependent oscillator]; Bhattacharjee & Gangopadhyay cm/05 [non-equilibrium sm]; Menezes & Svaiter JMP(06)ht [topological field theory]; Scarfone JSM(07)cm [interacting particle systems].

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