Carroll-Field-Jackiw term in nonlocal Lorentz-violating QED

Abstract

We investigate the radiative generation of the Carroll--Field--Jackiw (CFJ) term in nonlocal Lorentz- and CPT-violating extensions of quantum electrodynamics. Nonlocality is introduced in the fermionic sector through entire form factors depending on the Dirac operator. Using the Fréchet and derivative expansions of the one-loop fermionic determinant, we derive the induced CFJ contribution and analyze its ultraviolet behavior after Wick rotation. For one class of form factors, the loop integrals are absolutely convergent at finite nonlocality scale $Λ$, without requiring an additional UV regulator. For another class of form factors, the CFJ coefficient is defined through an Abel regularization prescription. In both cases, the CFJ structure is preserved and its coefficient is continuously modulated by the ratio between the fermion mass and the nonlocality scale. Thus, nonlocality removes the routing-, surface-term-, and UV-evanescent ambiguities of the finite-$Λ$ loop amplitude, although UV convergence alone does not imply complete prescription independence of the finite functional determinant.