Free scalar field theory on a Sobolev space over a bounded interval

IF 2.1 4区物理与天体物理 Q2 ASTRONOMY & ASTROPHYSICS

General Relativity and Gravitation Pub Date : 2024-05-30 DOI:10.1007/s10714-024-03256-2

J. Fernando Barbero G.

引用次数: 0

Abstract

This paper discusses several functional analytic issues relevant for field theories in the context of the Hamiltonian formulation for a free, massless, scalar field defined on a closed interval of the real line. The fields that we use belong to a Sobolev space with a scalar product. As we show this choice is useful because it leads to an explicit representation of the points in the fibers of the phase space (the cotangent bundle of the configuration space). The dynamical role of the boundary of the spatial manifold where the fields are defined is analyzed.

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有界区间索波列夫空间上的自由标量场论

本文以定义在实线闭区间上的自由、无质、标量场的哈密顿公式为背景，讨论了与场论相关的几个函数分析问题。我们使用的场属于具有标量积的索波列夫空间。正如我们所展示的，这种选择是有用的，因为它导致了相空间（构型空间的余切束）纤维中点的明确表示。我们分析了定义场的空间流形边界的动力学作用。

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

General Relativity and Gravitation 物理-天文与天体物理

CiteScore

4.60

自引率

3.60%

发文量

136

审稿时长

3 months

期刊介绍： General Relativity and Gravitation is a journal devoted to all aspects of modern gravitational science, and published under the auspices of the International Society on General Relativity and Gravitation. It welcomes in particular original articles on the following topics of current research: Analytical general relativity, including its interface with geometrical analysis Numerical relativity Theoretical and observational cosmology Relativistic astrophysics Gravitational waves: data analysis, astrophysical sources and detector science Extensions of general relativity Supergravity Gravitational aspects of string theory and its extensions Quantum gravity: canonical approaches, in particular loop quantum gravity, and path integral approaches, in particular spin foams, Regge calculus and dynamical triangulations Quantum field theory in curved spacetime Non-commutative geometry and gravitation Experimental gravity, in particular tests of general relativity The journal publishes articles on all theoretical and experimental aspects of modern general relativity and gravitation, as well as book reviews and historical articles of special interest.