Spontaneously Broken Lorentz Invariance in Three-Dimensional Gauge Theories
Yutaka Hosotani
TL;DR
This paper demonstrates that in certain three-dimensional Abelian gauge theories with a Chern-Simons term, Lorentz invariance is spontaneously broken, leading to a massless photon acting as a Nambu-Goldstone boson.
Contribution
It provides a detailed analysis of spontaneous Lorentz symmetry breaking and the emergence of a massless photon in three-dimensional gauge theories with a Chern-Simons term.
Findings
Lorentz invariance is spontaneously broken by a dynamical magnetic field.
The photon becomes massless, serving as a Nambu-Goldstone boson.
The energy density of the true vacuum is explicitly computed.
Abstract
In a wide class of three-dimensional Abelian gauge theories with a bare Chern-Simons term, the Lorentz invariance is spontaneously broken by dynamical generation of a non-vanishing magnetic field. A detailed computation of an energy density of the true vacuum is given. The originally massive photon becomes massless, fulfilling the role of a Nambu-Goldstone boson associated with the spontaneous breaking of the Lorentz invariance.
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