  A class of phenomenological relativistic models of hadronic systems motivated
by QCD that have dual representations as models of mesons and nucleons or
quarks and gluons is investigated. These models are designed to provided
qualitative insight into the role of sea quarks in hadronic structure and
reactions. The model assumption is that the Hamiltonian can be divided into two
parts; one that involves degrees of freedom in the same connected local and
global color singlet and the remaining interactions that allow the connected
local and global color singlets to interact. The first class of interactions
results in infinite towers of bare "particles" with hadronic quantum numbers.
All but a finite number of these remain stable when the second class of
interactions is included. The model interactions are expressed in terms of
sub-hadronic degrees of freedom, which determine the bare hadronic spectrum and
the interactions involving the bare hadrons in terms of a small number of
sub-hadronic model parameters. As a first test, this paper considers the
simplest case of mesons that interact via a string-breaking interaction. One
virtue of this model is that all of the bare meson masses and eigenfunctions
can be computed analytically. In addition, the string breaking interaction
leads to production vertices that can also be computed analytically. The
relativistic wave functions have a light-front kinematic symmetry. The goal is
to find a simple relativistic quantum mechanical model based on sub-hadronic
degrees of freedom that can provide an efficient, qualitatively consistent
description of hadronic masses, lifetimes, cross sections, sea quark effects,
and electromagnetic properties. The simplicity of the model makes it a
potentially useful tool to study the impact of sea quarks on hadronic structure
and reactions.
