Spontaneous breakdown of Lorentz symmetry in scalar QED with higher order derivatives

TL;DR

This paper explores how higher order derivatives in scalar QED lead to spontaneous Lorentz symmetry breaking, resulting in a novel vacuum structure and implications for gauge fields and Maxwell equations.

Contribution

It introduces a model where higher derivatives induce spontaneous Lorentz symmetry breaking in scalar QED, with a constructed vacuum and analysis of resulting gauge field dynamics.

Findings

Vacuum with non-zero scalar and vector expectation values breaks Lorentz symmetry.

Goldstone theorem ensures massless radiation fields despite symmetry breaking.

Standard Maxwell equations are recovered at tree level, with Lorentz violation effects appearing in radiative corrections.

Abstract

Scalar QED is studied with higher order derivatives for the scalar field kinetic energy. A local potential is generated for the gauge field due to the covariant derivatives and the vacuum with non-vanishing expectation value for the scalar field and the vector potential is constructed in the leading order saddle point expansion. This vacuum breaks the global gauge and Lorentz symmetry spontaneously. The unitarity of time evolution is assured in the physical, positive norm subspace and the linearized equations of motion are calculated. Goldstone theorem always keeps the radiation field massless. A particular model is constructed where the the full set of standard Maxwell equations is recovered on the tree level thereby relegating the effects of broken Lorentz symmetry to the level of radiative corrections.