Spontaneous breakdown of Lorentz invariance

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Abstract
We reexamine three-dimensional gauge theory with a Chern-Simons term in which Lorentz invariance is spontaneously broken by the dynamical generation of a magnetic field. A nonvanishing magnetic field leads, through the Nambu-Goldstone theorem, to a decrease in the zero-point energies of photons, which accounts for a major part of the mechanism. The asymmetric spectral flow plays an important role. The instability in pure Chern-Simons theory is also noted.
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