(-1)F

In a quantum field theory with fermions, (−1)^"F" is a unitary, Hermitian, involutive operator which multiplies 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.