The Weyl expansion for systems of independent identical particles

We present a novel analytical approach for the calculation of the mean density of states in many-body systems consisting of confined indistinguishable and independent particles. Our method makes explicit the intrinsic geometry inherent in the symmetrization postulate. In the spirit of the usual Weyl expansion for the smooth part of the density of states in confined single-particle systems, our results take the form of a sum over clusters of particles moving freely around manifolds in configuration space invariant under permutations. In our approach the emergence of the fermionic ground state is a consequence of a delicate cancellation effect of cluster contributions. As an asymptotic expansion, our approximation gives increasingly better results for large excitation energies, and we show that it coincides with the Bethe estimate in the appropriate region. Moreover, our construction gives the correct high-energy asymptotics expected from general considerations. Our expansion in cluster zones is naturally incorporated for systems of interacting particles, opening an alternative road to address the interplay between symmetry, confinement and interactions in many-body systems of identical bosonic or fermionic particles.