Role of Zero Modes in Quantization of QCD in Light-Cone Coordinates

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.