An integral formula of hyperbolic type for solutions of the Dirac equation on Minkowski space with initial conditions. (English) Zbl 1249.30122

The paper deals with the Dirac equation for spinor value fields on a Minkowski space of even dimension. It is shown how the solutions of this hyperbolic system of PDEs may be reconstructed from initial data given on the upper sheet of the hyperboloid \((x, x) = -R^2\), where \((\;,\;)\) stands for the Minkowski inner product. In particular, an integral formula is established expressing function values as an integral over a specific compact cycle.


30E20 Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane
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