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Physical Review

Summation Over Feynman Histories: Charged Particle in a Uniform Magnetic Field

M. L. Glasser

Published Feb 10, 1964• 27 citations
Publisher

Abstract

Using a particular parametrization of paths, the nonrelativistic propagator for a charged particle in a uniform magnetic field is derived by the Feynman method of summation over histories. It is shown that this sum is independent of the parameterization as long as the classical path is included. The result is used to obtain the density matrix for the system.

DOI
10.1103/physrev.133.b831

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International Journal of Modern Physics B•Nov 16, 2006•0 citations
Using a particular parametrization of paths, the nonrelativistic propagator for a charged particle in a uniform magnetic field is derived by the Feynman method of summation over histories. It is shown that this sum is independent of the parameterization as long as the classical path is included. The result is used to obtain the density matrix for the system.
Use of polar coordinates is examined in performing summation over all Feynman histories. Several relationships for the Lagrangian path integral and the Hamiltonian path integral are derived in the central-force problem. Applications are made for a harmonic oscillator, a charged particle in a uniform magnetic field, a particle in an inverse-square potential, and a rigid rotator. Transformations from Cartesian to polar coordinates in path integrals are rather different from those in ordinary calculus and this complicates evaluation of path integrals in polars. However, it is observed that for systems of central symmetry use of polars is often advantageous over Cartesians.