Constraints and Stability in Vector Theories with Spontaneous Lorentz Violation

TL;DR

This paper analyzes vector theories with spontaneous Lorentz violation, exploring their constraints, degrees of freedom, and stability, and compares them to electromagnetism to identify ghost-free models with positive Hamiltonian.

Contribution

It provides a Hamiltonian constraint analysis of bumblebee models, revealing conditions for stability and ghost-freedom, and compares their nonlinear gauge structure to electromagnetism.

Findings

Certain models are ghost-free with positive Hamiltonian.

The phase space matches electromagnetism in a nonlinear gauge.

Additional modes depend on the form of kinetic and potential terms.

Abstract

Vector theories with spontaneous Lorentz violation, known as bumblebee models, are examined in flat spacetime using a Hamiltonian constraint analysis. In some of these models, Nambu-Goldstone modes appear with properties similar to photons in electromagnetism. However, depending on the form of the theory, additional modes and constraints can appear that have no counterparts in electromagnetism. An examination of these constraints and additional degrees of freedom, including their nonlinear effects, is made for a variety of models with different kinetic and potential terms, and the results are compared with electromagnetism. The Hamiltonian constraint analysis also permits an investigation of the stability of these models. For certain bumblebee theories with a timelike vector, suitable restrictions of the initial-value solutions are identified that yield ghost-free models with a positive Hamiltonian. In each case, the restricted phase space is found to match that of electromagnetism in a nonlinear gauge.