caa a22 4500 469035145 CHVBK 20180323132754.0 cr unu---uuuuu 170328e19921101xx s 000 0 eng 10.1007/BF01083523 doi (NATIONALLICENCE)springer-10.1007/BF01083523 Kirillov A. aut On two mathematical problems of canonical quantization. IV [Elektronische Daten] [A. Kirillov] A method for solving the problem of reconstructing a measure beginning with its logarithmic derivative is presented. The method completes that of solving the stochastic differential equation via Dirichlet forms proposed by S. Albeverio and M. Rockner. As a result one obtains the mathematical apparatus for the stochastic quantization. The apparatus is applied to prove the existence of the Feynman-Kac measure of the sine-Gordon and λφ2n/(1 + K2φ2n)-models. A synthesis of both mathematical problems of canonical quantization is obtained in the form of a second-order martingale problem for vacuum noise. It is shown that in stochastic mechanics the martingale problem is an analog of Newton's second law and enables us to find the Nelson's stochastic trajectories without determining the wave functions. Plenum Publishing Corporation, 1992 Theoretical and Mathematical Physics Kluwer Academic Publishers-Plenum Publishers 93/2(1992-11-01), 1251-1261 0040-5779 93:2<1251 1992 93 11232 https://doi.org/10.1007/BF01083523 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF01083523 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Kirillov A. aut NATIONALLICENCE 773 0- Theoretical and Mathematical Physics Kluwer Academic Publishers-Plenum Publishers 93/2(1992-11-01), 1251-1261 0040-5779 93:2<1251 1992 93 11232 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer