Gauge Fixing Independence and the Partition Function of BF Theory: With an Application to the Analytic Torsion and the Ruelle Zeta Function

Abstract

In the first part of this thesis, we give an interpretation of the gauge-fixed partition function of a quantum field theory known as abelian BF theory in terms of certain regularized determinants. We proceed to formulate a partial statement concerning gauge fixing independence of the partition function and show how this result applies to the analytic torsion and the value at zero of the Ruelle zeta function. In the second part, we show how to recover the full Ruelle zeta function from perturbative quantum field theory, as the expectation value of a certain functional.