Physical basis of effective Abelian gauge theory of QCD

Abstract

Motivated by recent works of 't Hooft, we propose the nonlinear macroscopic Maxwell-Lorentz system, including magnetic-monopole matter, as a simple phenomenological replacement for a non-Abelian gauge theory system. Electric and magnetic charges may be defined through the Abelian projection for a non-Abelian gauge theory. The phase of the system is dictated by certain characteristic behaviors of the field-strength-dependent dielectric function $\ensuremath{\epsilon}$ at sufficiently weak field strengths. Here, $\ensuremath{\epsilon}$ can be expressed as the product $\ensuremath{\epsilon}={\ensuremath{\epsilon}}_{e}{\ensuremath{\epsilon}}_{m}$, with ${\ensuremath{\epsilon}}_{e}$ resulting from redistribution of electrically charged objects and ${\ensuremath{\epsilon}}_{m}$ from redistribution of magnetic monopoles. Magnetic-monopole matters tend to antiscreen free electric charges, and we relate this to antiscreening of quark colorelectric charges at relatively large-distance scale. Based on these ideas, we provide a theoretical basis of the effective Abelian gauge theory of QCD.