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Polar decomposition of the Wiener measure: Schwarzian theory versus conformal quantum mechanics. (English. Russian original) Zbl 1436.81030

Theor. Math. Phys. 200, No. 3, 1324-1334 (2019); translation from Teor. Mat. Fiz. 200, No. 3, 465-477 (2019).
Summary: We find an explicit form of the polar decomposition of the Wiener measure and obtain an equation relating functional integrals in conformai 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.

MSC:

81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
81R05 Finite-dimensional groups and algebras motivated by physics and their representations
57S05 Topological properties of groups of homeomorphisms or diffeomorphisms
28C20 Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.)
47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators
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