Geometry of the Constraint Sets for Yang–Mills–Dirac Equations with Inhomogeneous Boundary Conditions

Abstract:

The constraint equation for minimally coupled Yang–Mills and Dirac fields in bounded domains is studied under the inhomogeneous boundary conditions which admit unique solutions of the evolution equations. For each value of the boundary data, the constraint set is shown to be a submanifold of the extended phase space. It is a prinicipal fibre bundle over the reduced phase space with structure group consisting of the gauge symmetries which coincide on the boundary with the identity transformation up to the first order of contact.