St\"uckelberg inspired approach for avoiding singular Hamiltonians in Lorentz violating models of antisymmetric tensor field

TL;DR

This paper introduces a St"uckelberg-inspired auxiliary field to fix singular Hamiltonians in Lorentz-violating antisymmetric tensor field models, enabling their use in cosmology.

Contribution

It proposes a novel gauge-restoring approach using an auxiliary vector field to eliminate Hamiltonian singularities in these models.

Findings

Constraint matrix becomes non-singular on vacuum manifold

Restores gauge symmetry in Lorentz-violating models

Enables cosmological applications of the theory

Abstract

Spontaneous Lorentz violation models of antisymmetric tensor field are known to possess singular Hamiltonian on the vacuum manifold, leading to unresolvable pathologies that render such theories unfit for cosmological studies. In this work, we show that by introducing an auxiliary vector field inspired by the St\"uckelberg mechanism to restore the gauge symmetry of the Lagrangian, it is possible to resolve such pathologies on vacuum manifold. The constraint analysis using Dirac-Bergmann method leads to a constraint matrix that acquires dependence on gradients and conjugate momentum of the St\"uckelberg field and therefore remains non-singular on the vacuum manifold.