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Nonlinear vacuum electrodynamics and spontaneous breaking of Lorentz symmetry

C. A. Escobar

Instituto de Física, Universidad Nacional Autónoma de México, Apdo. Postal 20-364, Ciudad de México 01000, Mexico

E-mail Address: carlos_escobar@fisica.unam.mx

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and

R. Potting

http://orcid.org/0000-0001-6915-3994

Departamento de Física, Universidade do Algarve, FCT, 8005-139 Faro, Portugal

CENTRA, Instituto Superior Técnico, Universidade de Lisboa, Avenida Rovisco Pais, Lisboa, Portugal

E-mail Address: rpotting@ualg.pt

Corresponding author.

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https://doi.org/10.1142/S0217751X20501742Cited by:6 (Source: Crossref)

Abstract

We study spontaneous breaking of Lorentz symmetry in nonlinear vacuum electrodynamics. Using a first-order formulation of the latter proposed by Plebański, we apply a Dirac constraint analysis and derive an effective Hamiltonian. We show that there exists a large class of potentials for which the effective Hamiltonian is bounded from below, while at the same time possessing local minima in which the field strength acquires a nonzero vacuum expectation value, thereby breaking Lorentz invariance spontaneously. These possible vacua can be classified in four classes, depending on the way Lorentz symmetry is broken. We show that the small field fluctuations around these vacua involve modes for which the dynamics can develop degeneracies, resulting in shock-wave-like and/or superluminal motion. Finally, we study the physical applicability of these models, and show how the Lorentz breaking vacua might in principle be detected by coupling the model to a suitable external current, or to gravity.

Keywords:

PACS: 11.10.Lm, 11.30.Cp

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