Structure of radiatively induced Lorentz and [Formula Presented] violation in QED at finite temperature

We obtain the induced Lorentz- and (Formula presented)-violating term in QED at finite temperature using the imaginary-time formalism and dimensional regularization. Its form resembles a Chern-Simons-like structure, but, unexpectedly, it does not depend on the temporal component of the fixed (Formula presented) constant vector that is coupled to the axial-vector current. Nevertheless, Ward identities are respected and its coefficient vanishes at (Formula presented) consistent with previous computations with the same regularization procedure, and it is a nontrivial function of temperature. We argue that at finite T a Chern-Simons-like Lorentz- and (Formula presented)-violating term is generically present, the value of its coefficient being unambiguously determined up to a T-independent constant, related to the zero-temperature renormalization conditions. © 2001 The American Physical Society