BRST Quantisation and the Product Formula for the Ray-Singer Torsion
arXiv:hep-th/9310038 · doi:10.1142/S0217751X95000875
Abstract
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.
24 pages. TEX error of first version corrected: a \input is deleted