Geodesic
Path integral over branching paths
Teoretičeskaâ i matematičeskaâ fizika, Tome 45 (1980) no. 3, pp. 329-345 Cet article a éte moissonné depuis la source Math-Net.Ru

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A heuristic definition is given of a Feynman path integral over branching paths. It is used to solve the Cauchy problem for the model Hartree equation in a closed form. A number of properties of the solution are derived from an integral representation. In particular, the quasiclassical asymptotic behavior, the exact solution in the Gaussian case, and the perturbation series are described. An existence theorem is proved for the simplest path integral over branching paths. 
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V. P. Maslov; A. M. Chebotarev. Path integral over branching paths. Teoretičeskaâ i matematičeskaâ fizika, Tome 45 (1980) no. 3, pp. 329-345. http://geodesic.mathdoc.fr/item/TMF_1980_45_3_a3/

[1] B. A. Sevastyanov, Vetvyaschiesya protsessy, «Nauka», 1971 | MR

[2] R. Feinman, A. Khibbs, Kvantovaya mekhanika i integraly po traektoriyam, «Mir», 1968

[3] V. P. Maslov, Kompleksnye markovskie tsepi i kontinualnyi integral Feinmana, «Nauka», 1976 | MR

[4] Vo Khan Fuk, V. M. Chetverikov, TMF, 36 (1978), 345

[5] V. P. Maslov, Kompleksnyi metod VKB v nelineinykh uravneniyakh, «Nauka», 1977 | MR

[6] V. P. Maslov, TMF, 2 (1970), 30 | MR

[7] V. P. Maslov, M. V. Fedoryuk, Kvaziklassicheskoe priblizhenie dlya uravnenii kvantovoi mekhaniki, «Nauka», 1976 | MR