In the context of the nonminimal Standard Model extension a special subset of the $CPT$-even higher-dimensional operators in the photon sector is discussed from a quantum field theoretical point of view. The modified dispersion laws, photon polarization vectors and the gauge field propagator are obtained and their properties are analyzed. It is demonstrated that for certain sectors of the modified theory a puzzle arises for the optical theorem at tree level. This is followed by a discussion of how it can be interpreted and resolved at first order Lorentz violation. Furthermore the commutator of two gauge fields that are evaluated at different spacetime points is obtained and discussed. The structure of the theory is shown to resemble the structure of the modification based on the corresponding dimension-4 operator. However some properties are altered due to the nonrenormalizable nature of the theory considered. The results provide more insight into the characteristics of Lorentz-violating quantum field theories that rest upon contributions of nonrenormalizable dimension.

• Received 20 December 2013

DOI:https://doi.org/10.1103/PhysRevD.89.105019