Classical theory of canonical QCD on a space-like hypersurface

The canonical formalism in classical theory of QCD is constructed on a space-like hypersurface. The Poisson bracket on the space-like hypersurface is defined and it plays an important role to describe every algebraic relation in the canonical formalism into Lorentz covariant form. Surface integrals are introduced as alternatives of field equations for quarks, gluons, and Faddeev-Popov ghosts. It is shown that deformations of the space-like hypersurface for surface integrals are generated by the interaction term of QCD Hamiltonian density. By converting the Poisson bracket on the space-like hypersurface to four-dimensional commutator, we can pass over to QCD in the Heisenberg picture without spoiling the explicit Lorentz covariance.