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Proceedings of the Royal Society of London A Mathematical and Physical Sciences

Path integrals in polar coordinates

A. M. Arthurs

Published Nov 11, 1969• 22 citations
Publisher

Abstract

Abstract The problem of summation over Feynman histories in polar coordinates is discussed. Ordinary rules of calculus are used in conjunction with a Hamiltonian approach to the summation over histories. The procedure is checked by evaluating the propagator for a free particle in two dimensions.
DOI
10.1098/rspa.1969.0204

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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.
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