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(−1)F
In a quantum field theory with fermions, (−1)''F'' is a unitary, Hermitian, involutive operator where F is the fermion number operator and is equal to the sum of the lepton number plus the baryon number, F=B+L, for all particles in the Standard Model. The action of this operator is to multiply bosonic states by 1 and fermionic states by −1. This is always a global internal symmetry of any quantum field theory with fermions and corresponds to a rotation by 2π. This splits the Hilbert space into two superselection sectors. Bosonic operators commute with (−1)''F'' whereas fermionic operators anticommute with it.
This operator really shows its utility in supersymmetric theories. Its trace is often a useful computation.
==See also==
*Parity (physics)
*Primon gas
*Möbius function
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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