To bridge the gap between background-independent, non-perturbative quantum gravity and low-energy physics described by perturbative field theory in Minkowski spacetime, Minkowskian Fock states are located, analysed and used in the background-independent framework. This approach to the analysis of semiclassical issues is motivated by the recent results of Varadarajan (Varadarajan M and Zapata J A 2000 Class.?Quantum Grav.?17 4085-109). As in that work, we use the simpler U(1) example to illustrate our constructions but, in contrast to that work, we formulate the theory in such a way that it can be extended to full general relativity.

Relation between polymer and Fock excitations

We propose a way to extract the semi-classical approximation from nonrelativistic free quantum field theory formulated in a loop space. In this formulation we introduce the operators of the classical electromagnetic field, whose eigenvalues are the corresponding classical fields, and whose eigenfunctions are the coherent states. We also present arguments that suggest the adequacy of the loop space to study a system ofN independent oscillators in the continuum limit.

Classical amplitude operators of free quantum electrodynamics formulated in a loop space

In this work we present a study of the one-photon wave function and the coherent states in the formulation of second quantization of free electromagnetism in loop space. We obtain an explicit expression for the coherent states and calculate the mean values of the energy and the field with its standard deviations; we recover the classical values in the limit of a small fine structure constant.

G. M. Buendía

Papers

Coherent states and other basic states of quantum electrodynamics formulated in the loop space.