SU(3) Color Gauge Invariance and the Jaffe–Witten Mass Gap in QCD

Abstract

We discuss the role of group theory, the theory of distributions, and some theorems of the theory of functions of complex variable in connection with the so-called Jaffe–Witten mass gap in QCD, which is responsible for the large-scale structure of the QCD ground state and hence plays a dominant role in QCD as a theory of strong interactions at low energies. We show how the mass gap may appear without violating the SU(3) color gauge invariance of QCD. The theory of generalized functions (distributions) and the Weierstrass–Sochocki–Casorati theorem are used in order to perform the renormalization of the regularized mass gap.