A NOVEL SPIN-STATISTICS THEOREM IN (2 + 1)D CHERN SIMONS GRAVITY

It has been known for some time that topological geons in quantum gravity may lead to a complete violation of the canonical spin-statistics relation: There may be no connection between spin and statistics for a pair of geons. We present an algebraic description of quantum gravity in a (2 + 1)D manifold of the form Σ × ℝ, based on the first-order canonical formalism of general relativity. We identify a certain algebra describing the system, and obtain its irreducible representations. We then show that although the usual spin-statistics theorem is not valid, statistics is completely determined by spin for each of these irreducible representations, provided one of the labels of these representations, which we call flux, is superselected. We argue that this is indeed the case. Hence, a new spin-statistics theorem can be formulated.