LIGHT-FRONT QCD(1+1) COUPLED TO ADJOINT SCALAR MATTER

We consider adjoint scalar matter coupled to QCD(1+1) in light-cone qu antization on a finite 'interval' with periodic boundary conditions. W e work with the gauge group SU(2) which is modified to SU(2)/Z(2) by t he non-trivial topology. The model is interesting for various nonpertu rbative approaches because it is the sector of zero transverse momentu m gluons of pure glue QCD(2+1), where the scalar field is the remnant of the transverse gluon component. We use the Hamiltonian formalism in the gauge partial derivative_A(+) = 0. What survives is the dynamical zero mode of A(+), which in other theories gives topological structur e and degenerate vacua. With a point-splitting regularization designed to preserve symmetry under large gauge transformations, an extra A(+) dependent term appears in the current J(+). This is reminiscent of an (unwanted) anomaly. In particular, the gauge invariant charge and the similarly regulated P+ no longer commute with the Hamiltonian. We sho w that nonetheless one can construct physical states of definite momen tum which are not invariant under large gauge transformations but do t ransform in a well-defined way. As well, in the physical subspace we r ecover vanishing expectation values of the commutators between the gau ge invariant charge, momentum and Hamiltonian operators. It is argued that in this theory the vacuum is nonetheless trivial and the spectrum is consistent with the results of others who have treated the large N , SU(N), version of this theory in the continuum limit.