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SU(2) Yang-Mills Theory coupled to massive adjoint scalar matter is studiedin (1+1) dimensions using Discretised Light-Cone Quantisation. This theory canbe obtained from pure Yang-Mills in 2+1 dimensions via dimensional reduction.On the light-cone, the vacuum structure of this theory is encoded in thedynamical zero mode of a gluon and a constrained mode of the scalar field. Thelatter satisfies a linear constraint, suggesting no nontrivial vacua in thepresent paradigm for symmetry breaking on the light-cone. I develop adiagrammatic method to solve the constraint equation. In the adiabaticapproximation I compute the quantum mechanical potential governing thedynamical gauge mode. Due to a condensation of the lowest omentum modes of thedynamical gluons, a centrifugal barrier is generated in the adiabaticpotential. In the present theory however, the barrier height appears too smallto make any impact in this odel. Although the theory is superrenormalisable onnaive powercounting grounds, the removal of ultraviolet divergences isnontrivial when the constrained mode is taken into account. The open aspects ofthis problem are discussed in detail.Comment: LaTeX file, 26 pages. 14 postscript figure

Zero modes and the vacuum problem: A study of scalar adjoint matter in two-dimensional Yang-Mills theory via light-cone quantization