= Axial-current divergence for scalar and pseudoscalar backgrounds
{title2=$\partial_\mu j_5^\mu=2iS\bar\psi\gamma^5\psi+2P\bar\psi\psi$}
For $\mathcal L=\bar\psi(i\not\partial-S+iP\gamma^5)\psi$, with real scalar backgrounds $S,P$, the <Dirac equation> is $(i\not\partial-S+iP\gamma^5)\psi=0$ and the <adjoint Dirac equation> is $i(\partial_\mu\bar\psi)\gamma^\mu+S\bar\psi-iP\bar\psi\gamma^5=0$. Use $\{\gamma^5,\gamma^\mu\}=0$ and $(\gamma^5)^2=1$ in the derivative of $j_5^\mu=\bar\psi\gamma^\mu\gamma^5\psi$ to obtain the displayed classical identity. Taking $S=m+g\phi$ and $P=G\Phi$ includes both scalar and <Hermitian> pseudoscalar <Yukawa couplings>.
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