  Two-dimensional heavy-quark QCD is studied in the light-cone coordinates with
(anti-) periodic field boundary conditions. We carry out the light-cone
quantization of this gauge invariant model. To examine the role of the zero
modes of the gauge degrees of freedom, we consider the quantization procedure
in the zero mode and the nonzero mode sectors separately. In both sectors, we
obtain the physical variables and their canonical (anti-) commutation
relations. The physical Hamiltonian is constructed via a step-by-step
elimination of the unphysical degrees of freedom. It is shown that the zero
modes play a crucial role in the self-interaction potential of both the
heavy-quarks and gluons, and in the interaction potential between them. It is
also shown that the Faddeev-Popov determinant depends on the zero modes of the
gauge degrees of freedom. Therefore, one needs to introduce the Faddeev-Popov
ghosts in their own nonzero mode sector.
