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This paper specifically focuses on the choice of a temporal background fieldover a spatial one in the context of Lorentz symmetry breaking. By examiningthe implications of this choice, we aim to understand the effects of Lorentzviolation in different scenarios, with an emphasis on the consequences ofadopting a purely temporal background field. In the analysis of $\gamma$-pairproduction, a brief approach in QED is presented, exploring the production of apair of photons. Furthermore, the study investigates Lorentz violation withvectorial nonminimal coupling, analyzing the modifications introduced by thiscoupling in the scattering amplitude at the vertex. Additionally, Lorentzviolation with axial-like nonminimal coupling is explored, with a particularfocus. The additional coupling introduces further modifications to thescattering amplitude, highlighting the intricate nature of Lorentz symmetrybreaking in different scenarios.

Lorentz violation in $\gamma$-pair production ($e^{+}e^{-} \rightarrow \gamma\gamma$)