|
Parastatistics
In quantum mechanics and statistical mechanics, parastatistics is a hypothetical alternative to the established particle statistics models (Bose–Einstein statistics, Fermi–Dirac statistics and Maxwell–Boltzmann statistics). Other alternatives include anyonic statistics and braid statistics, both of these involving lower spacetime dimensions. Herbert S. Green is credited with the creation of parastatistics in 1953.H. S. Green, "A Generalized Method of Field Quantization", Phys. Rev. 90, 270–273 (1953). The particles predicted by parastatistics have not been experimentally observed. Formalism Consider the operator algebra of a system of ''N'' identical particles. This is a star-algebra, *-algebra. There is an ''SN'' group (symmetric group of order ''N'') Group action (mathematics), acting upon the operator algebra with the intended interpretation of permutation, permuting the ''N'' particles. Quantum mechanics requires focus on observables having a physical meaning, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Braid Statistics
In mathematics and theoretical physics, braid statistics is a generalization of the Spin–statistics theorem, 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 or even a non-trivial unitary transformation in the Hilbert space (see Anyon#Non-abelian anyons, non-Abelian anyons). A similar notion exists using a loop braid group. Plektons Braid statistics are applicable to theoretical particles such as the two-dimensional Anyon, anyons and plektons. A plekton is a hypothetical type of particle that obeys a different style of quantum statistics, statistics with respect to the interchange of identical particles. It obeys the causality rules of algebraic quantum field theory, where only observable quantities need to commute a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |