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Keywords:
Clifford analysis; integral formula of hyperbolic type; hyperboloid; Minkowski space
Clifford analysis; integral formula of hyperbolic type; hyperboloid; Minkowski space
Summary:
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 ${\mathbb{M}}$.
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