Path integrals in polar co-ordinates

Abstract

Functional integrals of the usual diffusion type in x ( t ), y ( t ), z ( t ) are discussed when transformed into polar co-ordinates r( t ), φ( t ), ϑ( t ). It is found that the functional integration can be performed directly but the limiting process of taking ∆ t → d t is more complicated than that encountered in normal integral and differential calculus, in particular terms of order (∆ t ) 2 cannot be neglected relative to terms of order (∆ t ).