Projective Statistics and Spinors in Hilbert Space

Frank Wilczek

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arXiv · hep-th/9806228

Projective Statistics and Spinors in Hilbert Space

Frank Wilczek

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Abstract

In quantum mechanics, symmetry groups can be realized by projective, as well as by ordinary unitary, representations. For the permutation symmetry relevant to quantum statistics of N indistinguishable particles, the simplest properly projective representation is highly non-trivial, of dimension $2^{(N-1)/2}$, and is most easily realized starting with spinor geometry. Quasiparticles in the Pfaffian quantum Hall state realize this representation. Projective statistics is a consistent theoretical possibility in any dimension.

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Frank Wilczek. 1998-06-29. Projective Statistics and Spinors in Hilbert Space. https://arxiv.org/abs/hep-th/9806228

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