Eliminating fermionic matter fields in lattice gauge theories

We devise a unitary transformation that replaces the fermionic degrees of freedom of lattice gauge theories by (hard-core) bosonic ones. The resulting theory is local and gauge invariant, with the same symmetry group. The method works in any spatial dimension and can be directly applied, among others, to the gauge groups G=U(N) and SU(2N), where N-N. For SU(2N+1), one can also carry out the transformation after introducing an extra idle Z2 gauge field, so that the resulting symmetry group trivially contains Z2 as a normal subgroup. Those results have implications in the field of quantum simulations of high-energy physics models.