An integral formula of hyperbolic type for solutions of the Dirac equation on Minkowski space with initial conditions on a hyperboloid

Martin Sikora

Address: Mathematical Institute, Charles University, Sokolovsk√° 83, Prague, Czech Republic

E-mail: sikora.martin@gmail.com

Abstract: The Dirac equation for spinor-valued fields $f$ on the Minkowski space of even dimension form a hyperbolic system of partial differential equations. In the paper, we are showing how to reconstruct the solution from initial data given on the upper sheet $H^+$ of the hyperboloid. In particular, we derive an integral formula expressing the value of $f$ in a chosen point $p$ as an integral over a compact cycle given by the intersection of the null cone with $H^+$ in the Minkowski space ${\mathbb{M}}$.

AMSclassification: primary 30E20.

Keywords: Clifford analysis, integral formula of hyperbolic type, hyperboloid, Minkowski space.