Diagram expansions in classical stochastic field theory. I. Regularisations, stochastic calculus and causal Wick's theorem
- 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.
Author: | L.I. Plimak, M. Fleischhauer, M.J. Collett |
---|---|
URN: | urn:nbn:de:hbz:386-kluedo-11491 |
Document Type: | Preprint |
Language of publication: | English |
Year of Completion: | 1999 |
Year of first Publication: | 1999 |
Publishing Institution: | Technische Universität Kaiserslautern |
Date of the Publication (Server): | 2001/05/15 |
Faculties / Organisational entities: | Kaiserslautern - Fachbereich Physik |
DDC-Cassification: | 5 Naturwissenschaften und Mathematik / 530 Physik |
Licence (German): | Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011 |