Lepton number

The lepton number LL is a quantum number representing leptons. It is 1 for leptons and -1 for antileptons. The lepton number is special in that it's actually three distinct numbers, one for each generation of leptons:

  1. Electronic lepton number LeL_{e}
  2. Muonic lepton number LμL_{\mu}
  3. Tau lepton number LτL_{\tau}

It is conserved in all interactions. More specifically, each lepton number is conserved separately, meaning that if a reaction involves more than one lepton generation, all of them need to conserve their own lepton number.

> The electronic lepton number is $0 \rightarrow 1 + 0 - 1$, so it is conserved, and the muonic lepton number is $1 \rightarrow 0 + 1 + 0$, which is also conserved. This reaction is therefore valid. > > Meanwhile, the decay > $$\mu^{-} \rightarrow e^{-} + \gamma

is impossible because, although it conserves all other quantities, it does not conserve the lepton number, which goes from Lμ=1,Le=0L_{\mu}=1,L_{e}=0 to Lμ=0,Le=1L_{\mu}=0,L_{e}=1.