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 dimensions and can be directly applied, among others, to the gauge groups $G=U(N)$ and $SU(2N)$, where $N\in\mathbb{N}$. For $SU(2N+1)$ one can also carry out the transformation after introducing an extra idle $\mathbb{Z}_2$ gauge field, so that the resulting symmetry group trivially contains $\mathbb{Z}_2$ as a normal subgroup. Those results have implications in the field of quantum simulations of high-energy physics models.