We develop an effective Lagrangian for the study of color-singlet hadrons which has some relation to quantum chromodynamics. We assume the QCD vacuum contains a condensate of gluon pairs, and introduce an order parameter χ(x), which describes the modification of this condensate in the presence of quarks. In addition, we introduce another order parameter which is related to the degree of local color neutrality of the system. We assume that there are kinetic terms in the effective Lagrangian for only the first of these order parameters, χ(x). Therefore the functional derivative of the effective Lagrangian with respect to the second-order parameter yields a constraint equation determining the value of the second-order parameter in terms of the (colored) quark current and the order parameter χ(x).

This analysis leads to a model in which the field that the quark sees has an attractive part dependent on χ(x), and a confining field that depends on ${\chi }^{\mathrm{-}2}$(x). While the equations of the model are nonlinear, they can be solved by iteration and yield a covariant description of a hadron. In this model the colored quark currents in a hadron are locally cancelled by screening currents. This leads to the vanishing of the coherent parts of ${\mathrm{E}}^a$(x) and ${\mathrm{B}}^a$(x), the color electric and magnetic fields. Thus we can remark that the QCD system can be thought of as both a perfect diamagnetic material (μ=0) and a perfect ‘‘dia-electric’’ material (ε=∞) when considering low-momentum-transfer phenomena. If we neglect the term describing confinement in (color-singlet) hadrons, the model described here reduces to our previously developed model of ‘‘covariant soliton dynamics,’’ a model which was able to give a good account of the structure of the nucleon and various mesons as (covariantly described) nontopological solitons.

The new feature that emerges in the work described here is a specific model for confinement related to the screening aspect of the theory noted above. While we have not derived this model from QCD we show in this work that our effective Lagrangian is not inconsistent with the highly nonlinear equations of QCD and may contain the key to understanding confinement in hadron physics. This situation is typical of that found in condensed-matter physics, where one does not solve the highly nonlinear equations of the theory but searches for the key elements governing the dynamics so that a model which explains the salient physical phenomena can be constructed.

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