Path integrals in polar co-ordinates

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 → dt 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).