Holomorphic Path Integrals in Tangent Space for Flat Manifolds

IF 0.5 Q4 PHYSICS, MATHEMATICAL

Journal of Geometry and Symmetry in Physics Pub Date : 2017-03-30 DOI:10.7546/jgsp-55-2020-21-37

Guillermo Capobianco, W. Reartes

引用次数: 0

Abstract

In this paper we study the quantum evolution in a flat Riemannian manifold. The holomorphic functions are defined on the cotangent bundle of this manifold. We construct Hilbert spaces of holomorphic functions in which the scalar product is defined using the exponential map. The quantum evolution is proposed by means of an infinitesimal propagator and the holomorphic Feynman integral is developed via the exponential map. The integration corresponding to each step of the Feynman integral is performed in the tangent space. Moreover, in the case of $S^1$, the method proposed in this paper naturally takes into account paths that must be included in the development of the corresponding Feynman integral.

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平面流形切线空间中的全纯路径积分

本文研究了平面黎曼流形中的量子演化。全纯函数定义在这个流形的余切丛上。我们构造了全纯函数的希尔伯特空间，其中标量积是用指数映射定义的。量子演化是用无穷小的传播子提出的，全纯费曼积分是用指数映射展开的。在切线空间中执行与费曼积分的每个步骤相对应的积分。此外，在$S^1$的情况下，本文提出的方法自然地考虑了在相应的费曼积分的发展中必须包括的路径。

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

Journal of Geometry and Symmetry in Physics PHYSICS, MATHEMATICAL-

CiteScore

1.50

自引率

25.00%

发文量

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