= Operator equation in a path integral
= Operator equation
{synonym}
An <operator equation in a path integral> $\mathcal O(x)=0$ asserts that insertions of $\mathcal O(x)$ vanish in every <time-ordered correlation function> with the other insertion points separated from $x$. Derivatives of <time ordering> can produce <Ward identity contact terms> at coincidence. For example, conservation of a <Dirac current> gives a vanishing separated-point divergence, while a charged insertion contributes a delta-function contact term fixed by its transformation. A vanishing one-point expectation value alone is insufficient.
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