The Faddeev-Popov procedure and application to bosonic strings: An infinite dimensional point of view

A generalisation of the finite dimensional presentation of the Faddeev-Popov perocedure is derived, in an infinite dimensional framework for gauge theories with finite dimensional moduli space using heat-kernel regularised determinants. It is shown that the infinite dimensional Faddeev-Popov determinant is-up to a finite dimensional determinant determined by a choice of a slice-canonically determined by the geometrical data defining the gauge theory, namely a fibre bundlePP/G with structure groupG and the invariance group of a metric structure given on the total spaceP. The case of (closed) bosonic string theory is discussed.