Spontaneous Lorentz Violation and Nonpolynomial Interactions
  Gauge-noninvariant vector field theories with superficially nonrenormalizable nonpolynomial interactions are studied. We show that nontrivial relevant and stable theories have spontaneous Lorentz violation, and we present a large class of asymptotically free theories. The Nambu-Goldstone modes of these theories can be identified with the photon, with potential experimental implications. 
B. Altschul and Alan Kostelecky