• Corpus ID: 131764856

Braid Group Statistics and their Superselection Rules

@inproceedings{RehrenBraidGS,
  title={Braid Group Statistics and their Superselection Rules},
  author={Karl-Henning Rehren}
}
We present recent results on the statistics in low-dimensional quantum field theory. They are described by unitary representations of the braid group. We discuss the structure of the “reduced field bundle” which is a charged field algebra exhibiting the braid group in its commutation relations (“exchange algebra”). We systematize results about the superselection rules for sectors with braid group statistics. 

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References

SHOWING 1-5 OF 5 REFERENCES

Space-time fields and exchange fields

We derive discrete symmetries of braid group statistics related to charge conjugation and outer automorphisms of the local algebra. The structure of the latter (which are abelian superselection

: in preparation . [ 10 ] V . F . R . Jones : Ann . Math .

    : Phys . Lett . 152 B , 88 ( 1985 )

      World Scientific ( Singapore ) 1987 ; Commun . Math . Phys . 28 , 331 ( 1972 )

      • 1986

      : “ The Energy - Momentum Tensor of Critical Quantum Field Theories in 1 + 1 Dimensions ”

      • 1976