Frölicher-smooth geometries, quantum jet bundles and BRST symmetry

Pubblicato online il 28 novembre 2014 - We attempt a clarification of geometric aspects of quantum field theory by using the no- tion of smoothness introduced by Frölicher and exploited by several authors in the study of functional bundles. A discussion of momentum and position representations in curved spacetime, in terms of generalized semi-densities, leads to a definition of quantum con- figuration bundle which is suitable for a treatment of that kind. A consistent approach to Lagrangian field theories, vertical infinitesimal symmetries and related currents is then de- veloped, and applied to a formulation of BRST symmetry in a gauge theory of the Yang–Mills type.