Method of steepest descent for path integrals
To estimate a Feynman path integral for a nonrelativistic particle with one degree of freedom in an arbitrary potential V(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 {open_quotes}contour of steepest descent,{close_quotes} 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.
- Sponsoring Organization:
- USDOE
- OSTI ID:
- 123319
- Journal Information:
- Theoretical and Mathematical Physics, Vol. 102, Issue 2; Other Information: PBD: Aug 1995; TN: Translated from Teoreticheskaya i Matematicheskaya Fizika; 102: No. 2, 210-216(Feb 1995)
- Country of Publication:
- United States
- Language:
- English
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