$L=ψˉ (iℏc∂/−mc_{2})ψ$

- $∂$: Feynman slash notation
- $ψˉ $: Dirac adjoint

Remember that $ψ$ is a 4-vetor, gamma matrices are 4x4 matrices, so the whole thing comes down to a dot product of two 4-vectors, with a modified $ψ$ by matrix multiplication/derivatives, and the result is a scalar, as expected for a Lagrangian.

Like any other Lagrangian, you can then recover the Dirac equation, which is the corresponding equations of motion, by applying the Euler-Lagrange equation to the Lagrangian.

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