Quantization and stability of bumblebee electrodynamics

TL;DR

This paper explores the quantization of a Lorentz-violating vector field model, employing the Stueckelberg trick and BRST symmetry, demonstrating a consistent, stable, and unitary reduced Fock space where the model aligns with Maxwell electrodynamics.

Contribution

It introduces a novel quantization framework for Lorentz-violating bumblebee electrodynamics, handling constraints via Stueckelberg and BRST methods, and establishes equivalence with Maxwell theory within a restricted Fock space.

Findings

A consistent quantization scheme is developed despite ghost and tachyon modes.

The model's free sector is shown to be equivalent to Maxwell electrodynamics in the temporal gauge.

A stable and unitary reduced Fock space is constructed for the theory.

Abstract

The quantization of a vector model presenting spontaneous breaking of Lorentz symmetry in flat Minkowski spacetime is discussed. The Stueckelberg trick of introducing an auxiliary field along with a local symmetry in the initial Lagrangian is used to convert the second-class constraints present in the initial Lagrangian to first-class ones. An additional deformation is employed in the resulting Lagrangian to handle properly the first-class constraints, and the equivalence with the initial model is demonstrated using the BRST invariance of the deformed Lagrangian. The framework for performing perturbation theory is constructed and the structure of the Fock space is discussed. Despite the presence of ghost and tachyon modes in the spectrum of the theory, it is shown that one can implement consistent conditions to define a unitary and stable reduced Fock space. Within the restricted Fock space, the free model turns out to be equivalent to the Maxwell electrodynamics in the temporal gauge.