The Fundamental Solution of the Hyperbolic Dirac Operator on $\mathbb{R}^{1,m}$ : a new approach

Abstract

In this paper, the fundamental solution of the Dirac equation on hyperbolic space will be calculated by means of the fundamental solution for the wave-operator in the $(m+1)$-dimensional Minkowski space-time of signature $(1,m)$. This leads to addition formulas for the fundamental solution in terms of the solution in a lower-dimensional Minkowski space-time. Certain identities between hypergeometric functions can then be used to obtain a closed form for the fundamental solution of the Dirac equation.