Path Integrals over Velocities in Quantum Mechanics
Abstract
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 spacetime 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 quasiGaussian integrals over velocities and rules of handling them. Such a technique allows one effectively calculate propagators in external fields. Thus, KleinGordon propagator is found in a constant homogeneous electromagnetic field and its combination with a plane wave field.
 Publication:

arXiv eprints
 Pub Date:
 October 1993
 arXiv:
 arXiv:hepth/9310074
 Bibcode:
 1993hep.th...10074G
 Keywords:

 High Energy Physics  Theory
 EPrint:
 26 pages, Preprint IFUSP/P1079 October 1993