  We propose an explicit formulation of the physical subspace for a
(1+1)-dimensional SU(2) lattice gauge theory, where the gauge degrees of
freedom are integrated out. Our formulation is completely general, and might be
potentially suited for the design of future quantum simulators. Additionally,
it allows for addressing the theory numerically with matrix product states. We
apply this technique to explore the spectral properties of the model and the
effect of truncating the gauge degrees of freedom to a small finite dimension.
In particular, we determine the scaling exponents for the vector mass.
Furthermore, we also compute the entanglement entropy in the ground state and
study its scaling towards the continuum limit.
