What is the most general reasonable form of the Lorentz invariant interaction term between a fermion field [tex]\psi[/tex] and a scalar field [tex]\phi[/tex]?(adsbygoogle = window.adsbygoogle || []).push({});

A common choice for the interaction is something like [tex]\psi^{\dagger}A\psi\phi[/tex], with [tex]A[/tex] being a Lorentz invariant matrix (like [tex]\gamma^{5}[/tex]). However, I don't see why an interaction couldn't include terms with arbitrary number of derivatives of fields, as long as it's Lorentz invariant (e.g. [tex]\partial_{\mu}\psi^{\dagger}A\partial^{\mu}\psi\phi[/tex] or [tex]\psi^{\dagger}A\partial_{\mu}\psi\partial^{\mu}\phi[/tex]).

Is there any physical reason for discarding such interaction terms with derivative coupling, or maybe we simply don't need them to describe real world interactions?

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# Fermion-scalar interaction

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