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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. ==Formalism== 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. For example in the case ''N'' = 2, ''R''2 − ''R''1 cannot be an observable because it changes sign if we switch the two particles, but the distance between the two particles : |''R''2 − ''R''1| is a legitimate observable. In other words, the observable algebra would have to be a *-subalgebra invariant under the action of ''SN'' (noting that this does not mean that every element of the operator algebra invariant under ''SN'' is an observable). Therefore we can have different superselection sectors, each parameterized by a Young diagram of ''SN''. In particular: * If we have ''N'' identical parabosons of order ''p'' (where ''p'' is a positive integer), then the permissible Young diagrams are all those with ''p'' or fewer rows. * If we have ''N'' identical parafermions of order ''p'', then the permissible Young diagrams are all those with ''p'' or fewer columns. * If ''p'' is 1, we just have the ordinary cases of Bose–Einstein and Fermi–Dirac statistics respectively. * If ''p'' is infinity (not an integer, but one could also have said arbitrarily large ''p''), we have Maxwell–Boltzmann statistics. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「parastatistics」の詳細全文を読む スポンサード リンク
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