Abstract
The perturbation theory for a color-quark gauge theory on a spatial lattice is developed in time-dependent form. Graphical rules are suggested. These methods are then applied to study the nature of the ${\ensuremath{\gamma}}_{5}$ symmetry exhibited when the bare-quark-mass term is zero. Investigation of the quark proper self-energy leads to the conclusion that the ${\ensuremath{\gamma}}_{5}$ symmetry is realized in the Nambu-Goldstone mode. A Bethe-Salpeter equation for the proper ${\ensuremath{\Gamma}}^{5}$ vertex is solved in the ladder approximation, and shown to exhibit zero-mass poles.
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