Dynamical ambiguities in models with spontaneous Lorentz violation

TL;DR

This paper investigates models with spontaneous Lorentz violation, revealing dynamical ambiguities that challenge the emergence of electromagnetic and gravitational interactions from such violations.

Contribution

It demonstrates the existence of non-unique evolution in spontaneous Lorentz violation models and discusses implications for emergent gravity and electromagnetism.

Findings

Initial data does not uniquely determine field evolution.

Hamilton density can be constructed to respect dynamical constraints.

Ambiguities can have observable physical effects.

Abstract

Spontaneous Lorentz violation is a viable mechanism to look for Planck scale physics. In this work, we study spontaneous Lorentz violation models, in flat spacetime, where a vector field produces such a violation and matter is modeled by a complex scalar field. We show that it is possible to construct a Hamilton density for which the evolution respects the dynamical constraints. However, we also find that the initial data, as required by standard field theory, does not determine the fields evolution in a unique way. In addition, we present some examples where the physical effects of such ambiguities can be recognized. As a consequence, the proposals in which the electromagnetic and gravitational interactions emerge from spontaneous Lorentz violation are challenged.