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