Quantum mechanics of the dynamical zero mode in (1+1)-dimensional QCD on the light cone

Motivated by the work of Kalloniatis, Pauli, and Pinsky, we consider the theory of light-cone quantized (1+1)-dimensional QCD on a spatial circle with periodic and antiperiodic boundary conditions on the gluon and quark fields, respectively. This approach is based on discretized light-cone quantization. We investigate the canonical structures of the theory. We show that the traditional light-cone gauge A-=0 is not available and the zero mode (ZM) is a dynamical field, which might contribute to the vacuum structure nontrivially. We construct the full ground state of the system and obtain the Schroedinger equation for the ZM in a certain approximation. Finally, the relationship between our results and those of Kalloniatis, Pauli, and Pinsky are discussed