Schwarzian functional integrals calculus

Schwarzian functional integrals calculus
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施瓦茨函数积分微积分

DOI:
10.1088/1751-8121/abbd52
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发表时间:
2019
期刊:
Journal of Physics A: Mathematical and Theoretical
影响因子:
--
通讯作者:
E. T. Shavgulidze
E. T. Shavgulidze
中科院分区:
--
文献类型:
--
作者:
V. Belokurov;E. T. Shavgulidze

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我们导出了Schwarzian类型理论中泛函积分的一般规则,从而完成了[,]中开创的Schwarzian泛函积分演算的阐述。我们的方法在数学上是严格的,不包含任何未经证明的猜想。它是基于对微分同胚群上的测度的性质的分析,而不是借鉴其他物理模型的经验。它的最大优点在于将泛函积分问题归结为唯一的泛函积分问题(),该问题是用以普通积分形式写出的结果显式计算的。我们在群Diff+1R和Diff+1(S1)上计算定义为泛函积分的两点和四点相关函数,并讨论了这两种情况下结果的差异。
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 [, ]. 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 () 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+1R and Diff+1(S1) , and discuss the difference between the results in the two cases.
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影响因子: 5.4
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