Abstract
In this paper, we study the one-loop induced photon’s effective action in the very special relativity electrodynamics in (2+1) spacetime (hbox {VSR}–hbox {QED}_{3}). Due to the presence of new nonlocal couplings resulting from the VSR gauge symmetry, we have additional graphs contributing to the langle AArangle and langle AAA rangle amplitudes. From these contributions, we discuss the VSR generalization of the Abelian Maxwell–Chern–Simons Lagrangian, consisting in the dynamical part and the Chern–Simons-like self-couplings, respectively. We use the VSR–Chern–Simons electrodynamics to discuss some non-Ohmic behavior on topological materials, in particular VSR effects on Hall’s conductivity. In the dynamical part of the effective action, we observe the presence of a UV/IR mixing, due to the entanglement of the VSR nonlocal effects to the quantum higher-derivative terms. Furthermore, in the self-coupling aspect, we verify the validity of the Furry’s theorem in the {hbox {VSR}}–hbox {QED}_{3} explicitly.
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