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- I'm just starting to work with QFT's and am trying to understand the construction of the Lagrangian's as well as how to read/work with them.

I'm just starting to get into QFT as some self study. I've watched some lectures and videos, read some notes, and am trying to piece some things together.

Take ##U(1)_{EM}: L = \bar{\psi}[i\gamma^{\mu}(\partial_{\mu} - ieA_{\mu}) - m]\psi - 1/4 F_{\mu\nu}F^{\mu\nu}##

This allegedly governs spin 1 bosons, where as something like the Klein-Gordon Lagrangian deals with spin 0 and Dirac deals with spin 1/2 (fermions).

It is extremely mysterious to me how to tell that one Lagrangian should govern one spin as opposed to another. The only thing that sticks out to me at all here are the gamma matrices, which act on spinors. However, a similar term is also present in the Dirac equation, so this can't be the full story. How does the "spin content" drop out?

Not sure whether to mark this as Intermediate or Advanced. I've studied both GR and QM so am familiar with the notation and the concepts in both, but am not all that familiar with quantum field theory, only a little bit with classical field theory.

Thanks

Take ##U(1)_{EM}: L = \bar{\psi}[i\gamma^{\mu}(\partial_{\mu} - ieA_{\mu}) - m]\psi - 1/4 F_{\mu\nu}F^{\mu\nu}##

This allegedly governs spin 1 bosons, where as something like the Klein-Gordon Lagrangian deals with spin 0 and Dirac deals with spin 1/2 (fermions).

It is extremely mysterious to me how to tell that one Lagrangian should govern one spin as opposed to another. The only thing that sticks out to me at all here are the gamma matrices, which act on spinors. However, a similar term is also present in the Dirac equation, so this can't be the full story. How does the "spin content" drop out?

Not sure whether to mark this as Intermediate or Advanced. I've studied both GR and QM so am familiar with the notation and the concepts in both, but am not all that familiar with quantum field theory, only a little bit with classical field theory.

Thanks