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. © 2023 World Scientific Publishing Company.