Gauge invariance of elementary particle processes taking place in presence of a background magnetic field

Elementary particle scatterings and decays in presence of a background magnetic field are very common in physics, specially after the observation that the core of the neutron stars can sustain a magnetic field of the order of $10^{13} {\rm G}$. The important point about these calculations is that they are done in a background of a gauge field and as a result the calculations are prone to gauge arbitrariness. In this work we will investigate how this gauge arbitrariness is eradicated in processes where the initial and final particles taking part in the interactions are electrically neutral. Some comments on those processes where the initial or final state consists of electrically charged particles is presented at the end of the article.