Dynamics on the SU(2) fundamental domain

For SU(2) gauge theory on the three-sphere we focus on a subspace of modes of the gauge field that contains the tunnelling paths and the sphalerons and on which the energy functional is degenerate to second order in the fields. The ultimate goal is to study the $\theta$-dependence of the low-lying states for this model by imposing boundary conditions on the fundamental domain.