Abstract
The central point of the paper is an isomorphism theorem which establishes a relation between a Gaussian random field associated with a symmetric Markov process (the free field) and local times for the process. The free field associated with the Brownian motion plays an important role in constructive quantum field theory. The isomorphism theorem allows one to express moments of the cutoff P(ϕ)2 fields in terms of multiple local times for the Brownian motion. On the other hand, techniques of field theory can be applied to investigate local times and self-crossing properties of Markov processes.
Research supported in part by NSF Grant MCS-8202286.
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© 1984 Birkhäuser Boston, Inc.
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Dynkin, E.B. (1984). Local Times and Quantum Fields. In: Çinlar, E., Chung, K.L., Getoor, R.K. (eds) Seminar on Stochastic Processes, 1983. Progress in Probability and Statistics, vol 7. Birkhäuser Boston. https://doi.org/10.1007/978-1-4684-9169-2_5
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DOI: https://doi.org/10.1007/978-1-4684-9169-2_5
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