SU(2) QCD in the Path Representation: General Formalism and Mandelstam Indentities

We introduce a path-dependent hamiltonian representation (the path representation) for SU(2) with fermions in 3 + 1 dimensions. The gauge-invariant operators and hamiltonian are realized in a Hilbert space of open path and loop functionals. We obtain two new types of Mandelstam identities one that connects open path operators with loop operators and other involving the end points of the paths.