Diffeomorphism Group Representations in Relativistic Quantum Field Theory

Abstract

We explore the role played by the diffeomorphism group and its unitary representations in relativistic quantum field theory. From the quantum kinematics of particles described by representations of the diffeomorphism group of a space-like surface in an inertial reference frame, we reconstruct the local relativistic neutral scalar field in the Fock representation. An explicit expression for the free Hamiltonian is obtained in terms of the Lie algebra generators (mass and momentum densities). We suggest that this approach can be generalized to fields whose quanta are spatially extended objects.

It has been an honor to present this talk in memory of my friend and colleague S. Twareque Ali, who passed away in January 2016. – G.A. Goldin