Diffeomorphism Groups, Topology, and Exotic Statistics of Quantum Particles
Diffeomorphism groups and their unitary representations provide a unifying framework (based on local symmetry) for a wide a variety of quantum-mechanical systems. This perspective leads naturally to an understanding of how and why exotic statistics come about. Examples beyond Bose and Femi statistics include parastatistics in physical spaces of dimension greater than one, and the “braid group” statistics of anyons and nonabelian anyons in two-dimensional spaces. One sees clearly the role played by configuration space topology in quantum kinematics. Generalization is natural to extended quantum configurations, including (for example) filaments and tubes of vorticity in superfluids.