Braid statistics

In mathematics and theoretical physics, braid statistics is a generalization of the spin statistics of bosons and fermions based on the concept of braid group. While for fermions (Bosons) the corresponding statistics is associated to a phase gain of $\pi$ ( $2\pi$ ) under the exchange of identical particles, a particle with braid statistics leads to a rational fraction of $\pi$ under such exchange ^[1]^[2] or even a non-trivial unitary transformation in the Hilbert space (see non-Abelian anyons). A similar notion exists using a loop braid group.

Braid statistics are applicable to theoretical particles such as the two-dimensional anyons and their higher-dimensional analogues known as plektons.

References

^ Leinaas, J. M.; Myrheim, J. (1977-01-01). "On the theory of identical particles". Il Nuovo Cimento B. 37 (1): 1–23. Bibcode:1977NCimB..37....1L. doi:10.1007/BF02727953. ISSN 1826-9877. S2CID 117277704.
^ Wilczek, Frank (1982-10-04). "Quantum Mechanics of Fractional-Spin Particles". Physical Review Letters. 49 (14): 957–959. Bibcode:1982PhRvL..49..957W. doi:10.1103/PhysRevLett.49.957.

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[1] Leinaas, J. M.; Myrheim, J. (1977-01-01). "On the theory of identical particles". Il Nuovo Cimento B. 37 (1): 1–23. Bibcode:1977NCimB..37....1L. doi:10.1007/BF02727953. ISSN 1826-9877. S2CID 117277704.

[2] Wilczek, Frank (1982-10-04). "Quantum Mechanics of Fractional-Spin Particles". Physical Review Letters. 49 (14): 957–959. Bibcode:1982PhRvL..49..957W. doi:10.1103/PhysRevLett.49.957.

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References