以 BF 理论表达的二维二次引力的哈密顿分析和法德耶夫-杰克夫形式主义

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

General Relativity and Gravitation Pub Date : 2024-05-24 DOI:10.1007/s10714-024-03249-1

Jaime Manuel Cabrera, Jorge Mauricio Paulin Fuentes

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引用次数: 0

摘要

我们研究了二维二次引力模型，它是背景场理论（BF）框架内对称性破缺的结果。该理论本质上是 BF 理论的扩展，引入了额外的多项式项，同时作用于规场和背景场。我们使用狄拉克和法德夫-雅基程序分析了这一理论，确定了轨距变换的形式、约束的完整结构、自由度的计算以及广义法德夫-雅基括号。此外，我们还证明了 Faddeev-Jackiw 和狄拉克括号的重合。最后，我们提出了一些评论并讨论了前景。

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Hamiltonian analysis and Faddeev–Jackiw formalism for two dimensional quadratic gravity expressed as BF theory

We examine the model of two-dimensional quadratic gravity as a consequence of symmetry breaking within the framework of background field (BF) theory. This theory is essentially an extension of BF theory, introducing an additional polynomial term that operates on both the gauge and background fields. We analyze the theory using the Dirac and Faddeev–Jackiw procedures, determining the form of the gauge transformation, the full structure of the constraints, the counting of degrees of freedom, and the generalized Faddeev–Jackiw brackets. Additionally, we demonstrate the coincidence of the Faddeev–Jackiw and Dirac’s brackets. Finally, we provide some remarks and discuss prospects.

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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.