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Green functions in stochastic field theory

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Abstract

Functional representations are reviewed for the generating function of Green functions of stochastic problems stated either with the use of the Fokker-Planck equation or the master equation. Both cases are treated in a unified manner based on the operator approach similar to quantum mechanics. Solution of a second-order stochastic differential equation in the framework of stochastic field theory is constructed. Ambiguities in the mathematical formulation of stochastic field theory are discussed. The Schwinger-Keldysh representation is constructed for the Green functions of the stochastic field theory which yields a functional-integral representation with local action but without the explicit functional Jacobi determinant or ghost fields.

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Authors and Affiliations

  1. National Defence University, Helsinki, Finland

    Juha Honkonen

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  1. Juha Honkonen
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Correspondence to Juha Honkonen.

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Honkonen, J. Green functions in stochastic field theory. Phys. Part. Nuclei 44, 349–359 (2013). https://doi.org/10.1134/S1063779613020172

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  • DOI: https://doi.org/10.1134/S1063779613020172

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