One-loop calculations in Lorentz-breaking theories and proper-time method

Abstract

We discuss applications of the proper-time method in various minimal Lorentz violating modifications of QED and present new results obtained with its use. Explicitly we calculate the complete one-loop Heisenberg-Euler effective action involving all orders in $F_{\mu\nu}$, for two of the most studied minimal Lorentz-violating extensions of QED, the one characterized by the axial vector $b^{\mu}$ and the one involving the second-rank constant tensor $c^{\mu\nu}$.

One-loop Schwinger effect in the presence of Lorentz-violating background fields

“…First we calculated the one-loop effective Lagrangian for the pure constant electric field case in the presence of the timelike b µ and the pseud-scalar m 5 Lorentz-violating background fields using the proper-time method. An interest result deduced from the effective Lagrangian (35) is the emergence of the CPT-even term (36), also found in the following works [13,42,56].…”

“…One readily notices that an CPT-even term is generated, a result previously encountered in [13,42,56].…”

“…Basically, it was shown that it was possible to start from the Lorentz and CPT violating fermionic sector of Quantum Electrodynamics (QED) and generate, through radiative correction, terms that also break CPT and Lorentz invariance. Many other works about such ideas can also be mentioned, [15,16,[34][35][36][37][38][39][40][41][42]. See also [43,44] for the non-Abelian case.…”

One-loop Schwinger effect in the presence of Lorentz-violating background fields

“…One readily notices that an CPT-even term is generated, a result previously encountered in [13,41,56].…”

“…Basically, starting from a Quantum Electrodynamics (QED) Lagrangian with violation of Lorentz and CPT symmetries in the fermionic sector (by radiative corrections and integrating out the fermion fields), new violation terms are generated in the electromagnetic sector. Many other works about such ideas can also be mena e-mail: rafaelljc@id.uff.br (corresponding author) b e-mail: rodrigo_sobreiro@id.uff.br tioned, [15,16,[34][35][36][37][38][39][40][41]. See also [42,43] for the non-Abelian case.…”