Projective Statistics in Quantum Gravity



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PIRSA Number: 
14050130

Abstract

To the extent that spacetime remains a manifold M on small scales, excitations of the spatial topology can function as particles called topological geons. In a first quantized theory of topological geons (aka continuum quantum gravity without topology change), different irreducible unitary representations of the mapping-class group G of M, yield different superselection sectors of the theory. In some of these sectors the geons behave as fermions, even though gravitons themselves are of course bosons. A still more exotic possibility is "projective statistics", where the operators that permute identical geons only preserve group multiplication up to a phase-factor that cannot be eliminated. (Such a representation must be nonabelian.) I will describe a simple example of this phenomenon with four RP^3 geons.