We consider the higher-derivative Lorentz-breaking extension of QED, where the new terms are the Myers-Pospelov-like ones in gauge and spinor sectors, and the higher–derivative Carroll-Field-Jackiw term. For this theory, we study its tree-level dynamics, discuss the dispersion relation, and present one more scheme for its perturbative generation, including the finite-temperature case. Also, we develop a method to study perturbative unitarity based on consistent rotation of the theory to Euclidean space. We use this method to verify explicitly that for special choices of the Lorentz-breaking vector the unitarity is preserved at the one-loop level, even in the presence of higher time derivatives.

• Received 25 April 2018
• Revised 25 March 2019

DOI:https://doi.org/10.1103/PhysRevD.99.096012

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Published by the American Physical Society