Dynamical ambiguities in models with spontaneous Lorentz violation

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.

Replaced to match the published version. 5 pages

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• Lorentz violation in the gravity sector: The t puzzle
• Vector models of gravitational Lorentz symmetry breaking
• Quantization and stability of bumblebee electrodynamics
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• Spontaneous symmetry breaking in models with second-class constraints
• Bumblebee gravity: spherically-symmetric solutions away from the potential minimum
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• Testing Lorentz symmetry with space-based gravitational-wave detectors
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