## (−1)^{F}

### ::concepts

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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.

**(−1)F sections**

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Fermion::books Operator::first Redir::press Location::google Onepage::false Title::''f''

{{#invoke:Message box|ambox}}

{{ safesubst:#invoke:Unsubst||$N=Merge |date=__DATE__ |$B= {{#invoke:Message box|mbox}} }}

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.

**(−1)F sections**

Intro See also References

PREVIOUS: Intro | NEXT: See also |

<< | >> |