Polar decomposition of the Wiener measure: Schwarzian theory versus conformal quantum mechanics

Evgeniy T. Shavgulidze; Vladimir V. Belokurov

Polar decomposition of the Wiener measure: Schwarzian theory versus conformal quantum mechanics

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arxiv 1812.04039 v3 pith:RSLOLPVS submitted 2018-12-10 hep-th

Vladimir V. Belokurov , Evgeniy T. Shavgulidze This is my paper · ORCID

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keywords conformalmechanicsquantumschwarziantheorydecompositionequationfunctional

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We derive the explicit form of the polar decomposition of the Wiener measure, and obtain the equation connecting functional integrals in conformal quantum mechanics to those in the Schwarzian theory. Using this connection we evaluate some nontrivial functional integrals in the Schwarzian theory and also find the fundamental solution of the Schroedinger equation in imaginary time in the model of conformal quantum mechanics.

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Schwarzian functional integrals calculus
hep-th 2019-08 conditional novelty 6.0 of 10

Schwarzian functional integrals over Diff^1_+(S^1)/SL(2,R) are reduced to ordinary integrals, giving two- and four-point correlators that do not factorize into two-point products.

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