Unitarity in a Lorentz symmetry breaking model with higher-order   operators
  We analyze the unitarity of a modified QED with higher-order terms that violate Lorentz symmetry. We make an explicit calculation to verify unitarity at the one-loop level. As expected we find negative norm states that could in principle lead to a violation of unitarity. However, we show that these states become massive in Euclidean space and do not contribute to the discontinuity. 
Markos Maniatis, Carlos M. Reyes
hep-ph