= Anti-self-dual Maxwell equations
{title2=$F_{AA'BB'}=\epsilon_{A'B'}\varphi_{AB},\quad \varphi_{AB}=\varphi_{BA}$}
= ASD Maxwell equations
{c}
{synonym}
In the <two-component spinor> convention with primed symmetric <gauge curvature> self-dual, an <Abelian> <Maxwell field> is anti-self-dual when its primed symmetric <gauge curvature> <two-component spinor> vanishes. For a locally exact field $F=dA$, the <Bianchi identity> gives $dF=0$; the duality relation then also gives $d{*}F=0$. Thus it obeys the source-free <Maxwell equations>. In complexified Lorentzian signature the <Hodge star> <eigenvalues> are $\pm i$; the <two-component spinor> condition specifies which component is meant without imposing a Euclidean eigenvalue on that signature.
// Destination: general-relativity.bigb
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