Meaning
The law of conservation of Lepton Number is the observation that in all fundamental interactions the sum of Leptons and Anti-leptons is the same before and after the interaction.
About Conservation of Lepton Number
- Leptons have a Lepton number of 1.
- Anti-leptons have a lepton number of -1.
- If a Lepton comes into existence an Anti-lepton must also come into existence.
- Conservation of Lepton Number can be applied to all fundamental interactions to balance the equations and to ascertain the types of particles produced.
Examples
\(p+\bar\nu_e\rightarrow n + \beta^+\)
|
|
\(p\)
|
\(+\)
|
\(\bar\nu_e\)
|
\(\rightarrow\)
|
\(n\)
|
\(+\)
|
\(\beta^+\)
|
| Charge
|
\(+1\)
|
\(+\)
|
\(0\)
|
\(=\)
|
\(0\)
|
\(+\)
|
\(+1\)
|
| Baryon Number
|
\(+1\)
|
\(+\)
|
\(0\)
|
\(=\)
|
\(+1\)
|
\(+\)
|
\(0\)
|
| Lepton Number
|
\(0\)
|
\(+\)
|
\(+1\)
|
\(=\)
|
\(0\)
|
\(+\)
|
\(+1\)
|
| Strangeness
|
\(0\)
|
\(+\)
|
\(0\)
|
\(=\)
|
\(0\)
|
\(+\)
|
\(0\)
|
\(n+\nu_e\rightarrow p + \beta^-\)
|
|
\(n\)
|
\(+\)
|
\(\nu_e\)
|
\(\rightarrow\)
|
\(p\)
|
\(+\)
|
\(\beta^-\)
|
| Charge
|
\(0\)
|
\(+\)
|
\(0\)
|
\(=\)
|
\(+1\)
|
\(+\)
|
\(-1\)
|
| Baryon Number
|
\(+1\)
|
\(+\)
|
\(0\)
|
\(=\)
|
\(+1\)
|
\(+\)
|
\(0\)
|
| Lepton Number
|
\(0\)
|
\(+\)
|
\(+1\)
|
\(=\)
|
\(0\)
|
\(+\)
|
\(+1\)
|
| Strangeness
|
\(0\)
|
\(+\)
|
\(0\)
|
\(=\)
|
\(0\)
|
\(+\)
|
\(0\)
|
\(p+\bar\nu_{\mu}\rightarrow n + \mu^+\)
|
|
\(p\)
|
\(+\)
|
\(\bar\nu_{\mu}\)
|
\(\rightarrow\)
|
\(n\)
|
\(+\)
|
\(\mu^+\)
|
| Charge
|
\(+1\)
|
\(+\)
|
\(0\)
|
\(=\)
|
\(0\)
|
\(+\)
|
\(+1\)
|
| Baryon Number
|
\(+1\)
|
\(+\)
|
\(0\)
|
\(=\)
|
\(+1\)
|
\(+\)
|
\(0\)
|
| Lepton Number
|
\(0\)
|
\(+\)
|
\(+1\)
|
\(=\)
|
\(0\)
|
\(+\)
|
\(+1\)
|
| Strangeness
|
\(0\)
|
\(+\)
|
\(0\)
|
\(=\)
|
\(0\)
|
\(+\)
|
\(0\)
|
\(n+\nu_{\mu}\rightarrow p + \mu^-\)
|
|
\(n\)
|
\(+\)
|
\(\nu_{\mu}\)
|
\(\rightarrow\)
|
\(p\)
|
\(+\)
|
\(\mu^-\)
|
| Charge
|
\(0\)
|
\(+\)
|
\(0\)
|
\(=\)
|
\(+1\)
|
\(+\)
|
\(-1\)
|
| Baryon Number
|
\(+1\)
|
\(+\)
|
\(0\)
|
\(=\)
|
\(+1\)
|
\(+\)
|
\(0\)
|
| Lepton Number
|
\(0\)
|
\(+\)
|
\(+1\)
|
\(=\)
|
\(0\)
|
\(+\)
|
\(+1\)
|
| Strangeness
|
\(0\)
|
\(+\)
|
\(0\)
|
\(=\)
|
\(0\)
|
\(+\)
|
\(0\)
|
\(p + e^- \rightarrow n + \nu_e\)
|
|
\(p\)
|
\(+\)
|
\(e^-\)
|
\(\rightarrow\)
|
\(n\)
|
\(+\)
|
\(\nu_e\)
|
| Charge
|
\(+1\)
|
\(+\)
|
\(-1\)
|
\(=\)
|
\(0\)
|
\(+\)
|
\(0\)
|
| Baryon Number
|
\(+1\)
|
\(+\)
|
\(0\)
|
\(=\)
|
\(+1\)
|
\(+\)
|
\(0\)
|
| Lepton Number
|
\(0\)
|
\(+\)
|
\(+1\)
|
\(=\)
|
\(0\)
|
\(+\)
|
\(+1\)
|
| Strangeness
|
\(0\)
|
\(+\)
|
\(0\)
|
\(=\)
|
\(0\)
|
\(+\)
|
\(0\)
|
\(p + \pi^- \rightarrow K^+ + \Sigma^-\)
|
|
\(p\)
|
\(+\)
|
\(\pi^-\)
|
\(\rightarrow\)
|
\(K^+\)
|
\(+\)
|
\(\Sigma^-\)
|
| Charge
|
\(+1\)
|
\(+\)
|
\(-1\)
|
\(=\)
|
\(+1\)
|
\(+\)
|
\(-1\)
|
| Baryon Number
|
\(+1\)
|
\(+\)
|
\(0\)
|
\(=\)
|
\(0\)
|
\(+\)
|
\(+1\)
|
| Lepton Number
|
\(0\)
|
\(+\)
|
\(0\)
|
\(=\)
|
\(0\)
|
\(+\)
|
\(0\)
|
| Strangeness
|
\(0\)
|
\(+\)
|
\(0\)
|
\(=\)
|
\(+1\)
|
\(+\)
|
\(-1\)
|
\(n + \pi^- \rightarrow K^0 + \Sigma^-\)
|
|
\(n\)
|
\(+\)
|
\(\pi^-\)
|
\(\rightarrow\)
|
\(K^0\)
|
\(+\)
|
\(\Sigma^-\)
|
| Charge
|
\(0\)
|
\(+\)
|
\(-1\)
|
\(=\)
|
\(0\)
|
\(+\)
|
\(-1\)
|
| Baryon Number
|
\(+1\)
|
\(+\)
|
\(0\)
|
\(=\)
|
\(0\)
|
\(+\)
|
\(+1\)
|
| Lepton Number
|
\(0\)
|
\(+\)
|
\(0\)
|
\(=\)
|
\(0\)
|
\(+\)
|
\(0\)
|
| Strangeness
|
\(0\)
|
\(+\)
|
\(0\)
|
\(=\)
|
\(+1\)
|
\(+\)
|
\(-1\)
|
\(n + \pi^+ \rightarrow K^+ + \Sigma^0\)
|
|
\(n\)
|
\(+\)
|
\(\pi^+\)
|
\(\rightarrow\)
|
\(K^+\)
|
\(+\)
|
\(\Sigma^0\)
|
| Charge
|
\(0\)
|
\(+\)
|
\(+1\)
|
\(=\)
|
\(+1\)
|
\(+\)
|
\(0\)
|
| Baryon Number
|
\(+1\)
|
\(+\)
|
\(0\)
|
\(=\)
|
\(0\)
|
\(+\)
|
\(+1\)
|
| Lepton Number
|
\(0\)
|
\(+\)
|
\(0\)
|
\(=\)
|
\(0\)
|
\(+\)
|
\(0\)
|
| Strangeness
|
\(0\)
|
\(+\)
|
\(0\)
|
\(=\)
|
\(+1\)
|
\(+\)
|
\(-1\)
|
\(p + \bar p \rightarrow \pi^+ + \pi^-\)
|
|
\(p\)
|
\(+\)
|
\(\bar p\)
|
\(\rightarrow\)
|
\(\pi^+\)
|
\(+\)
|
\(\pi^-\)
|
| Charge
|
\(+1\)
|
\(+\)
|
\(-1\)
|
\(=\)
|
\(+1\)
|
\(+\)
|
\(-1\)
|
| Baryon Number
|
\(+1\)
|
\(+\)
|
\(-1\)
|
\(=\)
|
\(0\)
|
\(+\)
|
\(0\)
|
| Lepton Number
|
\(0\)
|
\(+\)
|
\(0\)
|
\(=\)
|
\(0\)
|
\(+\)
|
\(0\)
|
| Strangeness
|
\(0\)
|
\(+\)
|
\(0\)
|
\(=\)
|
\(0\)
|
\(+\)
|
\(0\)
|
\(p\rightarrow n + \beta^+ + \nu_e\)
|
|
\(p\)
|
\(\rightarrow\)
|
\(n\)
|
\(+\)
|
\(\beta^+\)
|
\(+\)
|
\(\nu_e\)
|
| Charge
|
\(+1\)
|
\(=\)
|
\(0\)
|
\(+\)
|
\(+1\)
|
\(+\)
|
\(0\)
|
| Baryon Number
|
\(+1\)
|
\(=\)
|
\(+1\)
|
\(+\)
|
\(0\)
|
\(+\)
|
\(0\)
|
| Lepton Number
|
\(0\)
|
\(=\)
|
\(0\)
|
\(+\)
|
\(-1\)
|
\(+\)
|
\(+1\)
|
| Strangeness
|
\(0\)
|
\(=\)
|
\(0\)
|
\(+\)
|
\(0\)
|
\(+\)
|
\(0\)
|
\(n\rightarrow p + \beta^- + \bar\nu_e\)
|
|
\(n\)
|
\(\rightarrow\)
|
\(p\)
|
\(+\)
|
\(\beta^-\)
|
\(+\)
|
\(\bar\nu_e\)
|
| Charge
|
\(0\)
|
\(=\)
|
\(+1\)
|
\(+\)
|
\(-1\)
|
\(+\)
|
\(0\)
|
| Baryon Number
|
\(+1\)
|
\(=\)
|
\(+1\)
|
\(+\)
|
\(0\)
|
\(+\)
|
\(0\)
|
| Lepton Number
|
\(0\)
|
\(=\)
|
\(0\)
|
\(+\)
|
\(+1\)
|
\(+\)
|
\(-1\)
|
| Strangeness
|
\(0\)
|
\(=\)
|
\(0\)
|
\(+\)
|
\(0\)
|
\(+\)
|
\(0\)
|
\(\mu^+ \rightarrow e^+ + \bar\nu_{\mu}+\nu_{e}\)
|
|
\(\mu^+\)
|
\(\rightarrow\)
|
\(e^+\)
|
\(+\)
|
\(\bar\nu_{\mu}\)
|
\(+\)
|
\(\nu_{e}\)
|
| Charge
|
\(+1\)
|
\(=\)
|
\(+1\)
|
\(+\)
|
\(0\)
|
\(+\)
|
\(0\)
|
| Baryon Number
|
\(0\)
|
\(=\)
|
\(0\)
|
\(+\)
|
\(0\)
|
\(+\)
|
\(0\)
|
| Lepton Number
|
\(-1\)
|
\(=\)
|
\(-1\)
|
\(+\)
|
\(-1\)
|
\(+\)
|
\(+1\)
|
| Strangeness
|
\(0\)
|
\(=\)
|
\(0\)
|
\(+\)
|
\(0\)
|
\(+\)
|
\(0\)
|
\(\mu^- \rightarrow e^- + \nu_{\mu}+\bar\nu_{e}\)
|
|
\(\mu^-\)
|
\(\rightarrow\)
|
\(e^-\)
|
\(+\)
|
\(\nu_{\mu}\)
|
\(+\)
|
\(\bar\nu_{e}\)
|
| Charge
|
\(-1\)
|
\(=\)
|
\(-1\)
|
\(+\)
|
\(0\)
|
\(+\)
|
\(0\)
|
| Baryon Number
|
\(0\)
|
\(=\)
|
\(0\)
|
\(+\)
|
\(0\)
|
\(+\)
|
\(0\)
|
| Lepton Number
|
\(+1\)
|
\(=\)
|
\(+1\)
|
\(+\)
|
\(+1\)
|
\(+\)
|
\(-1\)
|
| Strangeness
|
\(0\)
|
\(=\)
|
\(0\)
|
\(+\)
|
\(0\)
|
\(+\)
|
\(0\)
|