Geodesic
Method of steepest descent for path integrals
Teoretičeskaâ i matematičeskaâ fizika, Tome 102 (1995) no. 2, pp. 210-216 Cet article a éte moissonné depuis la source Math-Net.Ru

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To estimate path integral for a nonrelativistic particle with one degree of freedom moving in a arbitrary potential $V(x)$ it is supposed to use the pass method, being an analog of the known pass method for finite-dimensional integrals, without transferring to the euclidean formulation of the theory. The notions of the functional Cauchy–Riemann conditions and the Cauchy theorem in a complex functional space are introduced. Given a contour of the most rapid descending the initial path integral is reduced to the one with the descending exponent. In principle, this result may serve as a base to construct a path integral measure. 
@article{TMF_1995_102_2_a3,
     author = {A. L. Koshkarov},
     title = {Method of steepest descent for path integrals},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {210--216},
     year = {1995},
     volume = {102},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1995_102_2_a3/}
}
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A. L. Koshkarov. Method of steepest descent for path integrals. Teoretičeskaâ i matematičeskaâ fizika, Tome 102 (1995) no. 2, pp. 210-216. http://geodesic.mathdoc.fr/item/TMF_1995_102_2_a3/