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

  • G.’t Hooft
Part of the NATO Advanced Study Institutes Series book series (NSSB, volume 59)


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.


Gauge Theory Magnetic Flux Gauge Transformation Topological Feature Perturbation Expansion 
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Copyright information

© Plenum Press, New York 1980

Authors and Affiliations

  • G.’t Hooft
    • 1
  1. 1.Institute for Theoretical PhysicsUtrechtThe Netherlands

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