Spontaneous symmetry breaking in Lorentz violating background

Abstract

In this paper, we study spontaneous symmetry breaking of gauge theories in a Lorentz violating background. Here, Lorentz symmetry will be broken down to its subgroup using the formalism of very special relativity. The breaking of the Lorentz symmetry will modify the gauge theories, and this will in turn modify the Higgs mechanisms for such theories. We will explicitly demonstrate that the different Hilbert spaces in various gauges of this theory can be related to each other through the gaugeon formalism. We will also discuss the FFBRST transformation for this theory, and observe that gaugeon formalism can be obtained from same. Thus, by making the BRST parameter finite and field dependent, we can relate different Hilbert spaces in different gauges for a gauge theory with spontaneous symmetry breaking in VSR.

Lorentz-violating gaugeon formalism for rank-2 tensor theory

“…One possible way to use the spontaneous symmetry-breaking mechanism to give a flavor-dependent VSR mass to the gauge bosons is also discussed [17,18]. An interesting VSR based description is proposed that VSR plays the same role for the field theoretic structure of dark matter as special relativity plays for standard model [19]. The VSR provides a new mechanism for neutrino mass which conserves lepton number without introducing additional sterile states [20].…”