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Fundamental solutions for the free Dirac electron and Einstein photonequations in position coordinates are constructed as matrix valued functionalson the space of bump functions. It is shown that these fundamental solutionsare related by a unitary transform via the Cauchy distribution in imaginarytime. We study the way the classical relativistic mechanics of the freeparticle comes from the quantum mechanics of the free Dirac electron.

Quantum mechanics of the free Dirac electrons and Einstein photons, and the Cauchy process