Yang-Mills theory in 2+1 dimensions: Coupling of matter fields and string-breaking effects

We explore further the Hamiltonian formulation of Yang-Mills theory in 2+1 dimensions in terms of gauge-invariant matrix variables. Coupling to scalar matter fields is discussed in terms of gauge-invariant fields. We analyze how the screening of adjoint (and other screenable) representations can arise in this formalism. A Schrödinger equation is then derived for the gluelump states which are the daughter states when an adjoint string breaks. A variational solution of this Schrödinger equation leads to an analytic estimate of the string-breaking energy which is within 8.8% of the latest lattice estimates.