Clifford Analysis with Indefinite Signature

We extend constructions of classical Clifford analysis to the case of indefinite non-degenerate quadratic forms. We define (p,q)-left- and right-monogenic functions by means of Dirac operators that factor a certain wave operator. We prove two different versions of Cauchy's integral formulas for these functions. The two formulas arise from dealing with singularities in distinct ways, and are inspired by the methods of [L, FL]. These results indicate the merit of these methods for dealing with singularities.