Spin and statistics in quantum gravity

Details Spin and statistics in quantum gravity Spin and statistics in quantum gravity

2001-01-11

arxiv.org/abs/gr-qc/0101042v1

Proceedings of the international meeting on ``Spin-statistics connections and commutation relations, experimental tests and th

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

14 pages, 4 figures, LaTeX

Scientific paper

We present a review of the spin and statistics of topological geons, particles in 3+1 quantum gravity. They can have half-odd-integral spin and fermionic statistics and since the underlying gravitational field is tensorial and bosonic, this is an example of ``emergent'' non-trivial spin and statistics as displayed by familiar non-gravitating objects such as skyrmions. We give the topological background and show that in a ``canonical'' quantization of gravity there is no spin-statistics correlation for topological geons. Allowing the topology of space to change, for example in a sum-over-histories approach, raises the possibility that a spin-statistics correlation can be recovered for geons. We review a conjectured set of rules powerful enough to give such a spin-statistics correlation for all topological geons. These would appear to rule out the possibility of parastatistics and may rule out spinorial and fermionic geons altogether.

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