Photons from quantized electric flux representations

Abstract

The quantum theory of U(1) connections admits a diffeomorphism invariant representation in which the electric flux through any surface is quantized. This representation is the analog of the representation of quantum SU(2) theory used in loop quantum gravity. We investigate the relation between this representation, in which the basic excitations are “polymerlike,” and the Fock representation, in which the basic excitations are wavelike photons. We show that normalizable states in the Fock space are associated with “distributional” states in the quantized electric flux representation. This work is motivated by the question of how wavelike gravitons in linearized gravity arise from polymerlike states in nonperturbative loop quantum gravity.