Geodesic
Polar decomposition of the~Wiener measure: Schwarzian theory versus conformal quantum mechanics
Teoretičeskaâ i matematičeskaâ fizika, Tome 200 (2019) no. 3, pp. 465-477

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We find an explicit form of the polar decomposition of the Wiener measure and obtain an equation relating functional integrals in conformal quantum mechanics to functional integrals in the Schwarzian theory. Using this relation, we evaluate some nontrivial functional integrals in the Schwarzian theory and also find the fundamental solution of the Schrödinger equation in imaginary time in the model of conformal quantum mechanics.
Keywords: Wiener measure, functional integral over the group of diffeomorphisms. 
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     author = {V. V. Belokurov and E. T. Shavgulidze},
     title = {Polar decomposition of {the~Wiener} measure: {Schwarzian} theory versus conformal quantum mechanics},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {465--477},
     publisher = {mathdoc},
     volume = {200},
     number = {3},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2019_200_3_a5/}
}
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V. V. Belokurov; E. T. Shavgulidze. Polar decomposition of the~Wiener measure: Schwarzian theory versus conformal quantum mechanics. Teoretičeskaâ i matematičeskaâ fizika, Tome 200 (2019) no. 3, pp. 465-477. http://geodesic.mathdoc.fr/item/TMF_2019_200_3_a5/