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On the stochastic quantization of field theory

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Abstract

We give a rigorous construction of a stochastic continuumP(φ)2 model in finite Euclidean space-time volume. It is obtained by a weak solution of a non-linear stochastic differential equation in a space of distributions. The resulting Markov process has continuous sample paths, and is ergodic with the finite volume EuclideanP(φ)2 measure as its unique invariant measure. The procedure may be called stochastic field quantization.

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Author notes

  1. G. Jona-Lasinio

    Present address: Dipartimento di Fisica, Università di Roma “La Sapienza,”, Piazzale Aldo Moro 2, I-00185, Roma, Italy

Authors and Affiliations

  1. Laboratoire de Physique Théorique et Hautes Energies, Université Pierre et Marie Curie, Paris VI, F-75230, Paris Cedex 05, France

    G. Jona-Lasinio & P. K. Mitter

Authors
  1. G. Jona-Lasinio
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  2. P. K. Mitter
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Additional information

Communicated by G. Mack

Laboratoire Associé 280 au CNRS

Supported in part by GNSM and INFN

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Jona-Lasinio, G., Mitter, P.K. On the stochastic quantization of field theory. Commun.Math. Phys. 101, 409–436 (1985). https://doi.org/10.1007/BF01216097

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  • DOI: https://doi.org/10.1007/BF01216097

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