Generalized theta series and monodromy of a Casimir connection. Case of rank 1

IF 1 4区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Theoretical and Mathematical Physics Pub Date : 2024-05-24 DOI:10.1134/s0040577924050015

E. I. Dotsenko

引用次数: 0

Abstract

The monodromy of the \(\mathfrak{sl}(2)\) Casimir connection is considered. It is shown that the trace of the monodromy operator over an appropriate space of flat sections gives the Jacobi theta constant and incomplete theta functions. A definition of new objects, namely, incomplete Appell–Lerch sums, is given, and their connection with the trace of the monodromy operator is revealed.

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卡西米尔连接的广义θ级数和单色性。秩 1 的情况

Abstract The monodromy of the \(\mathfrak{sl}(2)\)卡西米尔连接进行了研究。研究表明，在适当的平面截面空间上的单反转算子的迹给出了雅可比 Theta 常量和不完全 Theta 函数。给出了新对象的定义，即不完全阿贝尔-勒奇和，并揭示了它们与单旋转算子迹的联系。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Theoretical and Mathematical Physics 物理-物理：数学物理

CiteScore

1.60

自引率

20.00%

发文量

103

审稿时长

4-8 weeks

期刊介绍： Theoretical and Mathematical Physics covers quantum field theory and theory of elementary particles, fundamental problems of nuclear physics, many-body problems and statistical physics, nonrelativistic quantum mechanics, and basic problems of gravitation theory. Articles report on current developments in theoretical physics as well as related mathematical problems. Theoretical and Mathematical Physics is published in collaboration with the Steklov Mathematical Institute of the Russian Academy of Sciences.