Hamiltonian constraints and unfree gauge symmetry

V. Abakumova, S. Lyakhovich
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引用次数: 7

Abstract

We study Hamiltonian form of unfree gauge symmetry where the gauge parameters have to obey differential equations. We consider the general case such that the Dirac-Bergmann algorithm does not necessarily terminate at secondary constraints, and tertiary and higher order constraints may arise. Given the involution relations for the first-class constraints of all generations, we provide explicit formulas for unfree gauge transformations in the Hamiltonian form, including the differential equations constraining gauge parameters. All the field theories with unfree gauge symmetry share the common feature: they admit sort of "global constants of motion" such that do not depend on the local degrees of freedom. The simplest example is the cosmological constant in the unimodular gravity. We consider these constants as modular parameters rather than conserved quantities. We provide a systematic way of identifying all the modular parameters. We demonstrate that the modular parameters contribute to the Hamiltonian constraints, while they are not explicitly involved in the action. The Hamiltonian analysis of the unfree gauge symmetry is precessed by a brief exposition for the Lagrangian analogue, including explicitly covariant formula for degrees of freedom number count. We also adjust the BFV-BRST Hamiltonian quantization method for the case of unfree gauge symmetry. The main distinction is in the content of the non-minimal sector and gauge fixing procedure. The general formalism is exemplified by traceless tensor fields of irreducible spin $s$ with the gauge symmetry parameters obeying transversality equations.
哈密顿约束和非自由规范对称
研究了非自由规范对称的哈密顿形式,其中规范参数必须服从微分方程。我们考虑一般情况下,Dirac-Bergmann算法不一定终止于二级约束,三级和高阶约束可能出现。给出了所有代的一类约束的对合关系,给出了hamilton形式的非自由规范变换的显式公式,包括约束规范参数的微分方程。所有具有非自由规范对称的场论都有一个共同的特征:它们承认某种“整体运动常数”,这样就不依赖于局部自由度。最简单的例子是单模引力中的宇宙常数。我们认为这些常数是模参数而不是守恒量。我们提供了一种识别所有模块参数的系统方法。我们证明了模参数对哈密顿约束有贡献,而它们并没有显式地参与到动作中。对非自由规范对称的哈密顿分析进行了简要的阐述,包括自由度数计数的显式协变公式。我们还针对非自由规范对称调整了BFV-BRST哈密顿量子化方法。主要区别在于非最小扇区和量规固定程序的内容。用规范对称参数服从横向方程的不可约自旋$s$的无迹张量场举例说明了一般形式。
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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