  This paper is a follow-up to a previous paper on fermions. A simple state sum
model for a scalar field on a triangulated 1-manifold is constructed. The model
is independent of the triangulation and gives exactly the same partition
function as the continuum functional integral with zeta function
regularisation. For a certain choice of gauge group, the state sum model on the
circle is equivalent to the path integral for the simple harmonic oscillator.
