The Spin-Statistics Connection in Quantum Gravity

Abstract

It is well-known that is spite of sharing some properties with conventional particles, topological geons in general violate the spin-statistics theorem. On the other hand, it is generally believed that in quantum gravity theories allowing for topology change, using pair creation and annihilation of geons, one should be able to recover this theorem. In this paper, we take an alternative route, and use an algebraic formalism developed in previous work. We give a description of topological geons where an algebra of "observables" is identified and quantized. Different irreducible representations of this algebra correspond to different kinds of geons, and are labeled by a non-abelian "charge" and "magnetic flux". We then find that the usual spin-statistics theorem is indeed violated, but a new spin-statistics relation arises, when we assume that the fluxes are superselected. This assumption can be proved if all observables are local, as is generally the case in physical theories. Finally, we also show how our approach fits into conventional formulations of quantum gravity.

LaTeX file, 31 pages, 5 figures

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Cited by in corpus (5)

• Quantum Physics and Fluctuating Topologies: Survey
• A Novel Spin-Statistics Theorem in (2 + 1)d Chern-Simons Gravity
• Exotic Statistics for Ordinary Particles in Quantum Gravity
• Bosonic and fermionic behavior in gravitational configurations
• On the Failure of Spin-Statistics Connection in Quantum Gravity