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