Abstract
By using a new procedure representation formulas are obtained for the solution of the Cauchy problem for hyperbolic systems generalizing Schrödinger and Dirac equations. This procedure makes explicit the relation of the underlying Poisson jump process with the perturbation series. It allows one to find out a path integral representation formula for the two-dimensional Dirac equation. Further, it can be applied in the four-dimensional case with a Coulombian potential. This approach is also used to describe the time evolution of dissipative two-level systems and estimate transition probabilities.
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