On the disformal invariance of the Dirac equation

Abstract: In this paper we analyze the invariance of the Dirac equation under disformal transformations depending on the propagating spinor field. Using the Weyl-Cartan formalism, we construct a large class of disformal maps between different metric tensors, respecting the order of differentiability of the Dirac operator and satisfying the Clifford algebra in both metrics. Then, we have shown that there is a subclass of solutions of the Dirac equation, provided by Inomata's condition, which keeps the Dirac operator invariant under the action of the disformal group.