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