On the Possibility of Interaction of a Majorana Fermion with an Electromagnetic Field

Abstract

We propose a method for constructing a model of the interaction of the Majorana fermionic field of spin \({1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-0em} 2}\) with the photon field. It is shown that as well as for Dirac particles the electromagnetic field can be the gauge field also for Majorana ones. However, only if they are massless. A formulation of the model in which there are no dimensional parameters is given. Its most important features are discussed. The derivation of Ward’s identities is given. Feynman rules in coordinate representation are formulated and the possibility of using them for calculations is demonstrated. It is shown that in the considered model purely photon Green’s functions with odd number of arguments are equal to zero, what by virtue of Furry’s theorem, is fulfilled in quantum electrodynamics.