  We revisit the Jordan-Wigner transformation, showing that --rather than a
non-local isomorphism between different fermionic and spin Hamiltonian
operators-- it can be viewed in terms of local identities relating different
realizations of projection operators. The construction works for arbitrary
dimension of the ambient lattice, as well as of the on-site vector space,
generalizing Jordan-Wigner's result. It provides direct mapping of local
quantum spin problems into local fermionic problems (and viceversa), under the
(rather physical) requirement that the latter are described by Hamiltonian's
which are even products of fermionic operators. As an application, we
specialize to mappings between constrained-fermions models and spin 1 models on
chains, obtaining in particular some new integrable spin Hamiltonian, and the
corresponding ground state energies.
