Minimal coupling in presence of non-metricity and torsion
Minimal coupling in presence of non-metricity and torsion
复制标题
存在非公制度和扭转时的最小耦合
DOI：
10.1140/epjc/s10052-020-8330-y
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发表时间：
2020
期刊：
影响因子：
--
通讯作者：
Adrià Delhom
中科院分区：
文献类型：
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作者：
Adrià Delhom
我们讨论在存在扭转和/或非度规的情况下定义最小耦合处方意味着什么的问题，仔细解释了朴素的替换∂→∇\DocumentClass[12pt]{Minimum}\Usepackage{amsath}\Usepackage{amsFonts}\Usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathsfs}\usepackage{upgreek}\setLong{\oddsidemargin}{-69pt}\Begin{Document}$$\Partial\right tarrow\nabla$$\end{Document}在物质字段和连接之间引入了额外的耦合，在存在扭转和/或非元的情况下，这些连接可以被视为非最小。我们还将研究作用水平(MCpl)或场方程水平(MCPF)的最小耦合规定是否会导致不同的动力学。为此，我们将首先将物质场的欧拉-拉格朗日方程写成一般非黎曼空间的协变导数，并推导出相关的Noether电流和电荷的形式。然后我们将看到，如果像我们所讨论的那样应用最小耦合规定，对于自旋0和1场，MCp1和MCPF的结果是等价的，而对于自旋1/2场，如果应用MCPF或MCp1，则存在差异，因为前者导致电荷破坏。
We deal with the question of what it means to define a minimal coupling prescription in presence of torsion and/or non-metricity, carefully explaining while the naive substitution ∂→∇\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\partial \rightarrow \nabla $$\end{document} introduces extra couplings between the matter fields and the connection that can be regarded as non-minimal in presence of torsion and/or non-metricity. We will also investigate whether minimal coupling prescriptions at the level of the action (MCPL) or at the level of field equations (MCPF) lead to different dynamics. To that end, we will first write the Euler–Lagrange equations for matter fields in terms of the covariant derivatives of a general non-Riemannian space, and derivate the form of the associated Noether currents and charges. Then we will see that if the minimal coupling prescriptions is applied as we discuss, for spin 0 and 1 fields the results of MCPL and MCPF are equivalent, while for spin 1/2 fields there is a difference if one applies the MCPF or the MCPL, since the former leads to charge violation.