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

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