= Dirac fermion number conservation
{c}
{title2=$[Q,S]=0$}
= Fermion number conservation
{synonym}
A <Dirac field> theory invariant under $\psi\mapsto e^{i\alpha}\psi$, $\bar\psi\mapsto e^{-i\alpha}\bar\psi$ has a conserved global charge, subject to the quantum theory preserving the <symmetry>. In particle language this charge counts particles minus <antiparticles>. When the <S-matrix> commutes with it, a <scattering amplitude> between states of different charge vanishes. A neutral scalar and a <Yukawa interaction> preserve the charge, so a process with one incoming Dirac particle and only one outgoing Dirac antiparticle plus neutral particles is forbidden. This net charge is distinct from a sum of positive occupation numbers for all particle and antiparticle modes.
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