Fermion number ($Q=\int d^{3}x:{\psi }^{†}\psi :$)

For a Dirac field with a global phase symmetry, fermion number is the vacuum-subtracted charge of the Dirac current. In a mode expansion it counts particles minus antiparticles, with the overall sign fixed by the chosen generator convention. It is distinct from the total number of fermionic excitations and from fermion parity, which can survive even when interactions violate the continuous charge.