Fourier representation of a Kronecker delta (${\delta }_{nm}=(2\pi {)}^{-1}{\int }_0^{2\pi }{e}^{i(n-m)\theta }d\theta$)

Orthogonality of integer-frequency Fourier modes gives this identity: the integral is one for $n=m$ and zero otherwise. It converts integer step-count constraints into products of generating functions, as in the dilute-hopping lattice propagator.