The Eta Function in Chern-Simons Field Theory

We discuss a Schwinger expansion technique for computing the η-function of a first order operator in the pure Chern-Simons quantum field theory. When evaluated at zero, the η-function of this operator gives essentially the one-loop correction to the partition function. We illustrate this technique by explicitly computing the one-loop 2-point function in this theory on a fiat spacetime background