Imaginary-time path integrals for three magnetic relativistic Schrödinger operators

Abstract

After brief introduction to path integral, we consider the problem with three magnetic relativistic Schr\"odinger operators corresponding to the classical relativistic Hamiltonian symbol with magnetic vector and electric scalar potentials. We discuss their difference in general and their coincidence in the case of constant magnetic fields, as well as whether they are covariant under gauge transformation. Then results are surveyed on path integral representations for their respective imaginary-time relativistic Schr\"odinger equations, i.e. heat equations, by means of the probability path space measure coming from the L\’evy process concemed

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