标题： 带有洛伦兹和U(1)规范对称性破坏的电动力学及其哈密顿结构 显示英文标题

标题： Electrodynamics with violations of Lorentz and U(1) gauge symmetries and their Hamiltonian structure

摘要： 本文旨在研究标准模型扩展框架下的洛伦兹/U(1)规范对称性破缺的电动力学，并分析具有特定维度$d\leq 4$的洛伦兹破缺算符的理论的哈密顿结构。 为此，我们考虑包含洛伦兹/规范破缺算符的修改电动力学的一般二次作用量，并计算在规范不变性和破缺情况下不同维度的算符的独立分量数目。 通过这个一般作用量，我们进一步分析当考虑维度为$d\leq 4$的洛伦兹/规范破缺算符时，洛伦兹/规范对称性破缺如何改变理论的哈密顿结构。 我们证明，具有规范不变性的洛伦兹破缺算符不会改变理论的约束类别以及标准麦克斯韦电动力学的物理自由度数目。 当存在U(1)规范对称性破缺算符时，与标准麦克斯韦电动力学相比，理论通常缺乏第一类约束，并且多出一个额外的物理自由度。 显示英文摘要

摘要： This article aims to study the Lorentz/U(1) gauge symmetry-breaking electrodynamics in the framework of the Standard-Model Extension and analyze the Hamiltonian structure for the theory with a specific dimension $d\leq 4$ of Lorentz breaking operators. For this purpose, we consider a general quadratic action of the modified electrodynamics with Lorentz/gauge-breaking operators and calculate the number of independent components of the operators at different dimensions in gauge invariance and breaking. With this general action, we then analyze how the Lorentz/gauge symmetry-breaking can change the Hamiltonian structure of the theories by considering Lorentz/gauge-breaking operators with dimension $d\leq 4$ as examples. We show that the Lorentz-breaking operators with gauge invariance do not change the classes of the constraints of the theory and the number of the physical degrees of freedom of the standard Maxwell's electrodynamics. When the U(1) gauge symmetry-breaking operators are present, the theories in general lack first-class constraint and have one additional physical degree of freedom, compared to the standard Maxwell's electrodynamics.