Relativistic particles in curved space with a static metric using the Dunkl derivative in the Dirac operator

Abstract

In this paper, we introduce matrix operator algebra involving a universal curvature constant and using the Dunkl derivative. Consequently, the Dirac equation can be written without spin connections. Iterating the Dirac equation gives the Klein–Gordon equation in its canonical form without first-order Dunkl derivatives. This leads to a new form for the static metric based on the Dunkl operator in curved space.