Physics:Braid statistics
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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 [math]\displaystyle{ \pi }[/math] ([math]\displaystyle{ 2 \pi }[/math]) under the exchange of identical particles, a particle with braid statistics leads to a rational fraction of [math]\displaystyle{ \pi }[/math] 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.
See also
- Braid symmetry
- Parastatistics
- Anyon
References
- ↑ Leinaas, J. M.; Myrheim, J. (1977-01-01). "On the theory of identical particles" (in en). Il Nuovo Cimento B 37 (1): 1–23. doi:10.1007/BF02727953. ISSN 1826-9877. Bibcode: 1977NCimB..37....1L. https://doi.org/10.1007/BF02727953.
- ↑ Wilczek, Frank (1982-10-04). "Quantum Mechanics of Fractional-Spin Particles". Physical Review Letters 49 (14): 957–959. doi:10.1103/PhysRevLett.49.957. Bibcode: 1982PhRvL..49..957W. https://link.aps.org/doi/10.1103/PhysRevLett.49.957.
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