A. I. Kirillov, “Two mathematical problems of canonical quantization. III. Stochastic vacuum mechanics”, TMF, 91:3 (1992), 377–395; Theoret. and Math. Phys., 91:3 (1992), 591

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Teoreticheskaya i Matematicheskaya Fizika, 1992, Volume 91, Number 3, Pages 377–395 (Mi tmf5585)

This article is cited in 10 scientific papers (total in 10 papers)

Two mathematical problems of canonical quantization. III. Stochastic vacuum mechanics

A. I. Kirillov

Moscow Power Engineering Institute

Full-text PDF (1794 kB) Citations (10)

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Abstract: The problem of recovery of the measure from its logarithmic derivative is investigated. The role of this problem in stochastic mechanics, canonical quantization, and the theory of integration of functionals is discussed. It is shown that a measure that possesses logarithmic derivative

A

$A$ is a stationary distribution of a diffusion process with drift coefficient

A

$A$ . This makes it possible to calculate integrals with respect to the measure by means of Monte Carlo methods.

Received: 16.01.1992

English version:
Theoretical and Mathematical Physics, 1992, Volume 91, Issue 3, Pages 591–603
DOI: https://doi.org/10.1007/BF01017334

Bibliographic databases:

Language: Russian

Citation: A. I. Kirillov, “Two mathematical problems of canonical quantization. III. Stochastic vacuum mechanics”, TMF, 91:3 (1992), 377–395; Theoret. and Math. Phys., 91:3 (1992), 591–603

Citation in format AMSBIB

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\by A.~I.~Kirillov

\paper Two mathematical problems of canonical quantization.~III. Stochastic vacuum mechanics

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\yr 1992

\vol 91

\issue 3

\pages 377--395

\mathnet{http://mi.mathnet.ru/tmf5585}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1187017}

\transl

\jour Theoret. and Math. Phys.

\yr 1992

\vol 91

\issue 3

\pages 591--603

\crossref{https://doi.org/10.1007/BF01017334}

\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1992KL55200003}

Linking options:

https://www.mathnet.ru/eng/tmf5585

https://www.mathnet.ru/eng/tmf/v91/i3/p377

Cycle of papers

Two mathematical problems of canonical quantization. I
A. I. Kirillov
TMF, 1991, 87:1, 22–33
Two mathematical problems of canonical quantization. II
A. I. Kirillov
TMF, 1991, 87:2, 163–172
Two mathematical problems of canonical quantization. III. Stochastic vacuum mechanics
A. I. Kirillov
TMF, 1992, 91:3, 377–395
On two mathematical problems of canonical quantization. IV
A. I. Kirillov
TMF, 1992, 93:2, 249–263

This publication is cited in the following 10 articles:

Massimiliano Gubinelli, Encyclopedia of Mathematical Physics, 2025, 648
V. I. Bogachev, N. V. Krylov, M. Röckner, “Elliptic and parabolic equations for measures”, Russian Math. Surveys, 64:6 (2009), 973–1078
A. I. Kirillov, “Generalized differentiable product measures”, Math. Notes, 63:1 (1998), 33–49
A. I. Kirillov, “On the reconstruction of measures from their logarithmic derivatives”, Izv. Math., 59:1 (1995), 121–139
A. I. Kirillov, “Infinite-dimensional analysis and quantum theory as semimartingale calculus”, Russian Math. Surveys, 49:3 (1994), 43–95
A. I. Kirillov, “Field of sine-Gordon type in spacetime of arbitrary dimension: Existence of the nelson measure”, Theoret. and Math. Phys., 98:1 (1994), 8–19
A.I. Kirillov, “On the most probable paths of particles in stochastic mechanics”, Physics Letters A, 195:5-6 (1994), 277
E. P. Krugova, “On the integrability of logarithmic derivatives of measures”, Math. Notes, 53:5 (1993), 506–512
A. I. Kirillov, “Brownian motion with drift in a Hilbert space and its application in integration theory”, Theory Probab. Appl., 38:3 (1993), 529–533
A. I. Kirillov, “On two mathematical problems of canonical quantization. IV”, Theoret. and Math. Phys., 93:2 (1992), 1251–1261

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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Abstract page:	530
Full-text PDF :	172
References:	75
First page:	1

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