  We give a quantum field theoretic derivation of the formula obeyed by the
Ray-Singer torsion on product manifolds. Such a derivation has proved elusive
up to now. We use a BRST formalism which introduces the idea of an infinite
dimensional Universal Gauge Fermion, and is of independent interest being
applicable to situations other than the ones considered here. We are led to a
new class of Fermionic topological field theories. Our methods are also
applicable to combinatorially defined manifolds and methods of discrete
approximation such as the use of a simplicial lattice or finite elements. The
topological field theories discussed provide a natural link between the
combinatorial and analytic torsion.
