PHASE AND SCALING PROPERTIES OF DETERMINANTS ARISING IN TOPOLOGICAL FIELD-THEORIES

In topological field theory determinants of maps with negative as well as positive eigenvalues arise. We give a generalisation of the zeta-regularization technique to derive expressions for the phase and scaling-dependence of these determinants. For theories on odd-dimensional manifolds a simple formula for the scaling dependence is obtained in terms of the dimensions of cohomology spaces. This enables a non-perturbative feature of Chem-Simons gauge theory to be reproduced by semiclassical methods.