ON THE SCHRODINGER FUNCTIONAL IN QCD

In a series of publications (Nucl. Phys. B384 (1994) 168; B389 (1994) 247), Luscher et al. have demonstrated the usefulness of the Schroding er functional in pure SU(2) and SU(3) gauge theory. In this paper, it is shown how their formalism can be extended to include fermions. In t he framework of Wilson's lattice QCD, we define the Schrodinger functi onal by making use of the transfer matrix formalism. Boundary conditio ns for the fermions arise naturally. We then take the naive continuum limit of the action and show that no lattice peculiarities are left ov er. The corresponding free Dirac operator has a unique self-adjoint ex tension with purely discrete spectrum and no zero-modes.