  Hamiltonian simulations of quantum systems require a finite-dimensional
representation of the operators acting on the Hilbert space H. Here we give a
prescription for gauge links and canonical momenta of an SU(2) gauge theory,
such that the matrix representation of the former is diagonal in H. This is
achieved by discretising the sphere $S_3$ isomorphic to SU(2) and the
corresponding directional derivatives. We show that the fundamental commutation
relations are fulfilled up to discretisation artefacts. Moreover, we directly
construct the Casimir operator corresponding to the Laplace-Beltrami operator
on $S_3$ and show that the spectrum of the free theory is reproduced again up
to discretisation effects. Qualitatively, these results do not depend on the
specific discretisation of SU(2), but the actual convergence rates do.
