Geodesic
An integral formula of hyperbolic type for solutions of the Dirac equation on Minkowski space with initial conditions on a hyperboloid
Archivum mathematicum, Tome 46 (2010) no. 5, pp. 363-376

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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 ${\mathbb{M}}$.
Classification : 30E20, 30G35, 35Q41
Keywords: Clifford analysis; integral formula of hyperbolic type; hyperboloid; Minkowski space 
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     author = {Sikora, Martin},
     title = {An integral formula of hyperbolic type for solutions of the {Dirac} equation on {Minkowski} space with initial conditions on a hyperboloid},
     journal = {Archivum mathematicum},
     pages = {363--376},
     publisher = {mathdoc},
     volume = {46},
     number = {5},
     year = {2010},
     mrnumber = {2753990},
     zbl = {1249.30122},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2010__46_5_a6/}
}
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Sikora, Martin. An integral formula of hyperbolic type for solutions of the Dirac equation on Minkowski space with initial conditions on a hyperboloid. Archivum mathematicum, Tome 46 (2010) no. 5, pp. 363-376. http://geodesic.mathdoc.fr/item/ARM_2010__46_5_a6/