Induced Maxwell–Chern–Simons effective action in very special relativity

Abstract

Abstract In this paper, we study the one-loop induced photon’s effective action in the very special relativity electrodynamics in $$(2+1)$$ ( 2 + 1 ) spacetime ( $$\hbox {VSR}$$ VSR – $$\hbox {QED}_{3}$$ QED 3 ). Due to the presence of new nonlocal couplings resulting from the VSR gauge symmetry, we have additional graphs contributing to the $$\langle AA\rangle $$ ⟨ A A ⟩ and $$\langle AAA \rangle $$ ⟨ A A A ⟩ 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 $${\hbox {VSR}}$$ VSR – $$\hbox {QED}_{3}$$ QED 3 explicitly.