Background:
It is well known that the quantum mechanics of $n$ identical particles living on $\mathbb{R}^3$ can be obtained from the geometric quantization of the cotangent bundle of the manifold $M^n = \frac{\mathbb{R}^{3n}-\Delta}{S_n}$, where $\Delta$ is the set of coincidences and $S_n$ is the permutation group of $n$ elements acting naturally on the individual copies of $\mathbb{R}^3$, please see, for example, Souriau: Structure of dynamical systems. $T^*M^n$ is multiply connected with $\pi_1(T^*M^n) = S_n$. Given the canonical symplectic structure on $T^*M^n$,the set of inequivalent quantizations has a one to one correspondence to the set of character representations of the fundamental group $\mathrm{Hom}(\pi_1(M^n), U(1))= \mathbb{Z}_2$ corresponding to the identity and the parity characters. These quantizations correspond exactly to the pre-quantization of bosons and fermions. The boson and fermion Fock spaces modeled on $\mathrm{L}^2(R^3)$ emerge as the quantization of Hilbert spaces corresponding to these two possibilities.
Many authors pointed out that the removal of the coincidence set from the configuration space may seem not to be physically well motivated. The standard reasoning for this choice is that without the removal, the configuration space becomes an orbifold rather than a manifold. Some authors indicate also that without the removal, the configuration space is simply connected thus does allow only Bose quantization (Please, see for example the reprinted article by Y.S. Wu in Fractional statistics and anyon superconductivity By Frank Wilczek.
My question:
Are there any known treatments or results of the problem of geometric quantization of the configuration space as an orbifold (without the removal of the coincidence set), in terms of orbifold line bundles, etc.? Partial results or special cases are welcome. Does this quantization allow the possibility of Fermi statistics?