TL;DR
This paper explores how Lorentz violation in scalar quantum electrodynamics affects the Higgs mechanism, leading to Lorentz-violating gauge masses and potential superluminal propagation of gauge field modes.
Contribution
It introduces a framework for quantizing Lorentz-violating scalar QED in the Higgs phase, analyzing the implications for gauge field propagation and ghost field dynamics.
Findings
Lorentz-violating gauge mass terms arise from spontaneous symmetry breaking.
Longitudinal gauge modes can propagate superluminally.
Ghost field Lagrangian must also incorporate Lorentz violation.
Abstract
We consider scalar quantum electrodynamics in the Higgs phase and in the presence of Lorentz violation. Spontaneous breaking of the gauge symmetry gives rise to Lorentz-violating gauge field mass terms. These may cause the longitudinal mode of the gauge field to propagate superluminally. The theory may be quantized by the Faddeev-Popov procedure, although the Lagrangian for the ghost fields also needs to be Lorentz violating.
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