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Method of steepest descent for path integrals

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Abstract

To estimate a Feynman path integral for a nonrelativistic particle with one degree of freedom in an arbitrary potentialV(x), it is proposed to use a functional method of steepest descent, the analog of the method for finite-dimensional integrals, without going over to the Euclidean form of the theory. The concepts of functional Cauchy—Riemann conditions and Cauchy theorem in a complex function space are introduced and used essentially. After the choice in this space of a “contour of steepest descent,” the original Feynman integral is reduced to a functional integral of a decreasing exponential. In principle, the obtained result can serve as a basis for constructing the measure of Feynman path integrals.

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Authors
  1. A. L. Koshkarov
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Additional information

State University, Petrozavodsk. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 102, No. 2, pp. 210–216, February, 1995

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Koshkarov, A.L. Method of steepest descent for path integrals. Theor Math Phys 102, 153–157 (1995). https://doi.org/10.1007/BF01040395

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  • DOI: https://doi.org/10.1007/BF01040395

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