Instability in SU(2) gauge field theory

Abstract

Classical solutions to SU(2) gauge theory with a static charge source or with wave-like behavior are examined. In both cases gauge rotations cause instability. A quantum mechanical model with a local gauge symmetry is constructed. The quantum numbers of the model are constrained by the local symmetry. The S-matrix elements of SU(2) gauge theory are analysed in terms of angular orientation in gauge space. Most S-matrix elements are found to vanish in a way that indicates that most states are unstable. This result is due to the ambiguity in the time evolution of the states inherent in the local symmetry and it indicates that the gauge must be fixed in the path integral for a well defined dynamical evolution. When the gauge is fixed the result reduces to the conservation of quantised isospin.