On the disformal invariance of the Dirac equation

TL;DR

This paper investigates how the Dirac equation remains invariant under specific disformal transformations of the metric, identifying a subclass of solutions that preserve the Dirac operator through the disformal group.

Contribution

It introduces a class of disformal maps compatible with the Dirac equation and demonstrates invariance for solutions satisfying Inomata's condition.

Findings

Disformal transformations can preserve the Dirac operator for certain solutions.

A subclass of solutions maintains invariance under disformal maps.

The framework uses Weyl-Cartan formalism to relate different metrics.

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.