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Tue, 15 May 2001 00:00:00 +0200Tue, 15 May 2001 00:00:00 +0200Diagram expansions in classical stochastic field theory. I. Regularisations, stochastic calculus and causal Wick's theorem
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1216
Abstract: We aim to establish a link between path-integral formulations of quantum and classical field theories via diagram expansions. This link should result in an independent constructive characterisation of the measure in Feynman path integrals in terms of a stochastic differential equation (SDE) and also in the possibility of applying methods of quantum field theory to classical stochastic problems. As a first step we derive in the present paper a formal solution to an arbitrary c-number SDE in a form which coincides with that of Wick's theorem for interacting bosonic quantum fields. We show that the choice of stochastic calculus in the SDE may be regarded as a result of regularisation, which in turn removes ultraviolet divergences from the corresponding diagram series.L.I. Plimak; M. Fleischhauer; M.J. Collettpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1216Tue, 15 May 2001 00:00:00 +0200Diagram expansions in classical stochastic field theory / Diagram series and stochastic differential equations
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1217
We show that the solution to an arbitrary c-number stochastic differential equation (SDE) can be represented as a diagram series. Both the diagram rules and the properties of the graphical elements reflect causality properties of the SDE and this series is therefore called a causal diagram series. We also discuss the converse problem, i.e. how to construct an SDE of which a formal solution is a given causal diagram series. This then allows for a nonperturbative summation of the diagram series by solving this SDE, numerically or analytically.L.I. Plimak; M. Fleischhauer; M. J. Collettpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1217Tue, 15 May 2001 00:00:00 +0200