  In a class of renormalizable three-dimensional abelian gauge theory the
Lorentz invariance is spontaneously broken by dynamical generation of a
magnetic field $B$. The true ground state resembles that of the quantum Hall
effect. An originally topologically massive photon becomes gapless, fulfilling
the role of the Nambu-Goldstone boson associated with the spontaneous breaking
of the Lorentz invariance. We give a simple explanation and a sufficient
condition for the spontaneous breaking of the Lorentz invariance with the aid
of the Nambu-Goldstone theorem. The decrease of the energy density by $B \not=
0$ is understood mostly due to the shift in zero-point energy of photons. For
PASCOS'94.
