 Quartic Yukawa interaction in three spacetime dimensions

A nonderivative interaction of two real scalar legs with a fermion pair in $2+1$ dimensions. The engineering dimensions of relativistic fields are $[\varphi ]=1/2$ and $[\psi ]=1$, so $g$ is a marginal coupling by classical power counting. The internal symmetry $\varphi \mapsto -\varphi$ forbids odd-scalar interactions, but allows a sextic scalar interaction. The two-component Dirac field representation must be distinguished from four-component gamma matrices in four spacetime dimensions.