An invariance argument for confinement (Q1897815)

This paper develops an approach to the problem of cofinement in quantum chromodynamics based on non-abelian gauge invariance and the locality axiom of quantum field theory. This approach is based on knowledge of the structure of the classical field theory together with an understanding of the process of quantization. A quantum field theory is said to be confining if it does not allow for a description of the spatial separation of charges. The authors show that for Yang-Mills-Dirac fields in Minkowski space, gauge-invariant charge densities depend non-locally on the field variables and have non-local Poisson brackets unless the color label belongs to the center of the color algebra. For Yang-Mills-Dirac fields in a bounded domain, the color algebra is trivial and the color changes vanish identically. Thus, the Yang-Mills-Dirac theory can be considered confining on the basis of purely mathematical arguments.