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I need some help to find the correct symmetrized Lagrangian for the field operators. After some work I guess that

$$\mathcal{L} = i[\overline{\psi}_a,({\partial_\mu}\gamma^\mu \psi)^a] -m[\overline{\psi}_a,\psi^a ]$$

should be the correct Lagrangian but I'm not sure with this.

I'm also intrested in the question of reordinger this Lagrangian in such a way that all [itex]\overline{\psi}[/itex] are on the left and all [itex]\psi[/itex] are on the right side. My problem: I don't know how to deal with products like [itex](\partial_\mu \gamma^\mu \psi) \overline{\psi}[/itex]

Thanks for your help.

Neutrino

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# I Symmetrized Lagrangian (second quantization)

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