Narrow Results

Very Special Relativity (VSR), proposed by Cohen and Glashow, considers one of the subgroups of Poincaré group as the symmetry of spacetime. This paper investigates the transformations of electromagnetic fields under boosts of VSR, and by the aid of them studies the interaction energy between spin of an electron and external electromagnetic fields. Here, we argue that Thomas precession, one of the consequences of Special Relativity (SR), does not exist in HOM(2) avatar of VSR. The predictions of SR and VSR about the spin interaction energy in a certain case are compared, and despite the absence of Thomas precession in VSR, no noticeable departure is seen.

In Very Special Relativity (VSR), the neutrino mass term is coupled with the VSR preferred axis, and hence Lorentz violating in nature. Beyond standard model physics predicts neutrino magnetic moment which is linearly proportional to the mass eigenstates of the neutrinos. We report an additive kinematic phase in the neutrino flavor oscillation due to the neutrino magnetic moment in the VSR framework. This phase is proportional to the coupling between the VSR preferred axis with the external magnetic field as well as the spin of the neutrino. Furthermore, we predict time variation in the neutrino oscillation with a period of one sidereal day.

In this paper, we will study the Lorentz symmetry breaking down to its subgroup. A two-form gauge theory is investigated in the Lorentz violating background and it will be shown that this symmetry violation affects the structure of this gauge theory. In particular, we will study the gaugeon formalism and FFBRST for such a theory in this broken spacetime. In addition to Kugo-Ojima type condition, a thorough evaluation of quantum gauge freedom and gaugeon modes is carried out. We will explicitly demonstrate that in Lorentz broken spacetime, our reducible gauge theory fully depicts the physical aspects of gaugeon fields.

A time-dependent strain induces non-Abelian gauge field in a sheet of graphene. We discuss the effective field theory of this system of graphene subjected to a general form of time-dependent strain. We study the modifications to this effective field theory as a result of breaking Lorentz symmetry down to its sub-group, $SIM(1)$, employing the VSR formalism. As the effective theory describing the graphene system has gauge symmetry; to quantize this theory, we add a suitable ghost and gauge fixing terms to the original action. The resultant action is observed to be invariant under a BRST symmetry. We have studied the BRST symmetry of the resultant theory, and explicitly constructed the BRST transformations.