We use a Hodge decomposition and its generalization to non-abelian fla
t vector bundles to calculate the partition function for abelian and n
on-abelian BF theories in n dimensions. This enables us to provide a s
imple proof that the partition function is related to the Ray-Singer t
orsion defined on flat vector bundles for all odd-dimensional manifold
s and is equal to unity for even dimensions. (C) 1994 Academic Press,
Inc.