  Cavity QED models are analyzed in terms of field quadrature operators. We
demonstrate that in such representation, the problem can be formulated in terms
of effective gauge potentials. In this respect, it presents a completely new
system in which gauge fields arise, possessing the advantages of purity, high
control of system parameters as well as preparation and detection methods.
Studying three well known models, it is shown that either Abelian or
non-Abelian gauge potentials can be constructed. The non-Abelian
characteristics are evidenced via numerical simulations utilizing experimental
parameters.
