Geometric quantization and the Bogoliubov transformation

Abstract

This paper treats some simple applications of geometric quantization theory to problems involving the interaction of quantum fields with ex­ternal classical potentials. The main new result is a representation of the transition amplitudes for a boson field in terms of functional integrals over the classical phase space (the space of solutions of the classical field equations). An analogous representation for fermion fields is also con­structed.