  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.
