V. V. Belokurov, E. T. Shavgulidze, “Polar decomposition of the Wiener measure: Schwarzian theory versus conformal quantum mechanics”, TMF, 2019, Volume 200, Number 3,Pages <nobr>465

This article is cited in 3 papers

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

V. V. Belokurov^ab, E. T. Shavgulidze^a

^a Lomonosov Moscow State University, Moscow, Russia
^b Institute for Nuclear Research, Russian Academy of Sciences, Moscow, Russia

Abstract: 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.

Received: 14.12.2018
Revised: 14.12.2018

DOI: 10.4213/tmf9677