High Quality Content by WIKIPEDIA articles! In quantum mechanics and statistical mechanics, parastatistics is one of several alternatives to the better known 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. Consider the operator algebra of a system of N identical particles. This is a *-algebra. There is an SN group (symmetric group of order N) acting upon the operator algebra with the intended interpretation of permuting the N particles. Quantum mechanics requires focus on observables having a physical meaning, and the observables would have to be invariant under all possible permutations of the N particles.

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