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), $\varphi$(t), $\vartheta$(t). It is found that the functional integration can be performed directly but the limiting process of taking $\Delta$t$\rightarrow$ dt is more complicated than that encountered in normal integral and differential calculus, in particular terms of order ($\Delta$t)$^2$ cannot be neglected relative to terms of order ($\Delta$t).