  Non-abelian gauge theories play an important role in the standard model of
particle physics, and unfold a partially unexplored world of exciting physical
phenomena. In this letter, we suggest a realization of a non-abelian lattice
gauge theory - SU(2) Yang-Mills in 1+1 dimensions, using ultracold atoms.
Remarkably, and in contrast to previous proposals, in our model gauge
invariance is a direct consequence of angular momentum conservation and thus is
fundamental and robust. Our proposal may serve as well as a starting point for
higher dimensional realizations.
