Stückelberg inspired approach for avoiding singular Hamiltonians in Lorentz violating models of antisymmetric tensor field

TL;DR

Spontaneous Lorentz violation in antisymmetric tensor field theories can produce a singular Hamiltonian on the vacuum manifold, complicating evolution and quantization. The authors implement a Stückelberg-inspired gauge restoration by introducing an auxiliary vector field $C_a$, enabling a Dirac-Bergmann constraint analysis that reveals a constraint matrix $M_{ij}$ whose structure now depends on gradients and the conjugate momentum of the Stückelberg field. This dependence prevents singularity on the vacuum manifold, and explicit vacuum analysis shows $M^{-1}$ exists even when a gauge $C_a=0$ is imposed, enabling well-defined Hamiltonian dynamics. The work provides a path toward ghost-free, quantizable Lorentz-violating models and motivates future exploration of higher-derivative extensions and quantum effects.

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 Stückelberg 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 Stückelberg field and therefore remains non-singular on the vacuum manifold.