Geodesic
Sine-Gordon type field in spacetime of arbitrary dimension.~II:~Stochastic quantization
Teoretičeskaâ i matematičeskaâ fizika, Tome 105 (1995) no. 2, pp. 179-197

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Using the theory of Dirichlet forms we prove the existence of a distribution-valued diffusion process such that the Nelson measure of a field with bounded interaction density is its invariant probability measure. A Langevin equation in mathematically correct form is formulated which is satisfied by the process. The drift term of the equation is interpreted as a renormalized Euclidean current operator. 
@article{TMF_1995_105_2_a0,
     author = {A. I. Kirillov},
     title = {Sine-Gordon type field in spacetime of arbitrary {dimension.~II:~Stochastic} quantization},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {179--197},
     publisher = {mathdoc},
     volume = {105},
     number = {2},
     year = {1995},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1995_105_2_a0/}
}
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A. I. Kirillov. Sine-Gordon type field in spacetime of arbitrary dimension.~II:~Stochastic quantization. Teoretičeskaâ i matematičeskaâ fizika, Tome 105 (1995) no. 2, pp. 179-197. http://geodesic.mathdoc.fr/item/TMF_1995_105_2_a0/