Divergence-free quantum electrodynamics in locally conformally flat space-time

Abstract

This paper describes an approach to quantum electrodynamics (QED) in curved space–time obtained by considering infinite-dimensional algebra bundles associated to a natural principal bundle Q associated with any locally conformally flat space–time, with typical fibers including the Fock space and a space of fermionic multiparticle states which forms a Grassmann algebra. Both these algebras are direct sums of generalized Hilbert spaces. The requirement of K covariance associated with the geometry of space–time, where K is the structure group of Q, leads to the consideration of K intertwining operators between various spaces. Scattering processes are associated with such operators and are encod..