Which Topological Features of a Gauge Theory can be Responsible for Permanent Confinement?

Abstract

In the previous lecture a simple gauge model was considered with a scalar field doublet ξ. Perturbation expansion was considered not about the point ξ = o but about the “vacuum value”

$$\varepsilon =\left\{ \begin{matrix} F\\o\\\end{matrix} \right\}. $$

. Such a theory is usually called a theory with “spontaneous symmetry breakdown” ¹⁾. In contrast one might consider “unbroken gauge theories” where perturbation expansion is only performed about a symmetric “vacuum”. These theories are characterized by the absence of a mass term for the gauge vector bosons in the Lagrangian. The physical consequences of that are quite serious. The propagators now have their poles at k² = o and it will often happen that in the diagrams new divergences arise because such poles tend to coincide. These are fundamental infrared divergences that imply a blow-up of the interactions at large distance scales. Often they make it nearly impossible to understand what the stable particle states are.