Path Integrals over Velocities in Quantum Mechanics

Details Path Integrals over Velocities in Quantum Mechanics Path Integrals over Velocities in Quantum Mechanics

1993-10-13

arxiv.org/abs/hep-th/9310074v1

Physics

High Energy Physics

High Energy Physics - Theory

26 pages, Preprint IFUSP/P-1079 October 1993

Scientific paper

Representations of propagators by means of path integrals over velocities are discussed both in nonrelativistic and relativistic quantum mechanics. It is shown that all the propagators can only be expressed through bosonic path integrals over velocities of space-time coordinates. In the representations the integration over velocities is not restricted by any boundary conditions; matrices, which have to be inverted in course of doing Gaussian integrals, do not contain any derivatives in time, and spinor and isospinor structures of the propagators are given explicitly. One can define universal Gaussian and quasi-Gaussian integrals over velocities and rules of handling them. Such a technique allows one effectively calculate propagators in external fields. Thus, Klein-Gordon propagator is found in a constant homogeneous electromagnetic field and its combination with a plane wave field.

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