Electrodynamics with violations of Lorentz and U(1) gauge symmetries and their Hamiltonian structures* *Supported by the National Key Research and Development Program of China (2020YFC2201503, the Zhejiang Provincial Natural Science Foundation of China (LR21A050001, LY20A050002) and the National Natural Science Foundation of China (12275238, 11675143). B.-F. Li is supported by the National Natural Science Foundation of China (NNSFC) (12005186)

Abstract

This study aims to investigate 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 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 Lorentz/gauge symmetry-breaking can change the Hamiltonian structure of the theories by considering Lorentz/gauge-breaking operators with dimension as examples. We show that the Lorentz-breaking operators with gauge invariance do not change the classes of the theory constrains and the number of physical degrees of freedom of the standard Maxwell electrodynamics. When U(1) gauge symmetry-breaking operators are present, the theories generally lack a first-class constraint and have one additional physical degree of freedom compared to the standard Maxwell electrodynamics.