Physics Asked by Hao on October 1, 2020

I often heard that electron-muon scattering is a QED process. So I suppose that muon is a field in QED. However, when looking at the QED Lagrangian, it is basically

F^2 + psi D_A psi

where D_A is the gauge covariant derivative (with gamma matrices). Since psi already represents the electron, my question is, where is the muon?

Is it just "another copy" of Fermionic field, so that the Lagrangian looks something like the following?

F^2 + psi_1 D_A psi_1 + psi_2 D_A psi_2

Assuming there's no muon decay or other weak or strong interactions (i.e. the only interactions were electromagnetic), then yes, the Lagrangian would consist of the EM tensor term and two charged Dirac fermion terms as you have written above. The only difference would be the mass: $m_e$ in one and $m_mu$ in the other.

Answered by probably_someone on October 1, 2020

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