Functional integration over the factor-space $Diff^{1}_{+}(S^{1})/SL(2,\textbf{R}) $

TL;DR

This paper derives an explicit measure on a specific factor space of diffeomorphisms of the circle, simplifying the calculation of Schwarzian functional integrals and enhancing their transparency.

Contribution

It provides a new explicit form of the functional measure on the factor space $Diff^{1}_{+}(S^{1})/SL(2, extbf{R})$, improving the computational approach.

Findings

Explicit measure simplifies Schwarzian integrals

Enhanced transparency in functional calculus

Facilitates further research in related geometric structures

Abstract

An explicit form of the functional measure on the factor space $Diff^{1}_{+}(S^{1})/SL(2,\textbf{R})$ is obtained that makes Schwarzian functional integrals calculus simpler and more transparent.