Schwarzian泛函积分
Schwarzian functional integrals calculus
摘要：
我们导出了Schwarzian型理论中函数积分的一般规则，从而完成了\cite{(BShExact)}，\cite{(BShCorrel)}中开创的Schwarzian函数积分微积分的阐述。我们的方法在数学上是严格的，不包含任何未经证明的假设。它是基于对复同态群上测度性质的分析，不需要其他物理模型的经验。它的最大优点在于将泛函积分问题简化为唯一的泛函积分（\ref{E}）问题，该泛函积分是用普通积分的形式显式计算的。我们评估两点和四点关联函数定义为功能积分的组$Diff^{1}_{+}(\textbf{R}) $和$Diff^{1}_{+}(S^{1})\,,$，并讨论在这两种情况下的结果之间的差异。
英文摘要：
We derive the general rules of functional integration in the theories of Schwarzian type, thus completing the elaboration of Schwarzian functional integrals calculus initiated in \cite{(BShExact)}, \cite{(BShCorrel)}. Our approach is mathematically rigorous and does not contain any unproved conjectures. It is based on the analysis of the properties of the measures on the groups of diffeomorphisms, and does not appeal for the experience from other physical models. Its great merit consists in reducing a problem of functional integration to that of the only functional integral (\ref{E}) that is calculated explicitly with the result written in the form of the ordinary integral. We evaluate two-point and four-point correlation functions defined as functional integrals over the groups $Diff^{1}_{+}(\textbf{R}) $ and $Diff^{1}_{+}(S^{1})\,,$ and discuss the difference between the results in the two cases.
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