  Renormalization group procedure for effective particles (RGPEP) is applied in
terms of a second-order perturbative computation to an Abelian gauge theory, as
an example of application worth studying on the way toward derivation of a
dynamical connection between the spectroscopy of bound states and their
parton-model picture in the front form of Hamiltonian dynamics. In addition to
the ultraviolet transverse divergences that are handled using the RGPEP in
previously known ways, the small-x divergences are handled by introducing a
mass parameter and a third polarization state for gauge bosons using a
mechanism analogous to spontaneous breaking of global gauge symmetry, in a
special limit that simplifies the theory to Soper's front form of massive QED.
The resulting orders of magnitude of scales involved in the dynamics of
effective constituents or partons in the simplified theory are identified for
the fermion and boson mass counter terms, effective masses and
self-interactions, as well as for the Coulomb-like effective interactions in
bound states of fermions. Computations in orders higher than second are
mentioned but not described in this article.
