= BRST-closed operator
{c}
= BRST-closed
{c}
{synonym}
A BRST-closed operator is annihilated by the differential defining a <BRST transformation>: $sO=0$. In operator language, $sO$ is a graded <commutator> with the <BRST charge>, so closure does not generally mean the ordinary product $QO$ vanishes.
Physical local observables are sought in the ghost-number-zero <BRST cohomology>: a closed operator is identified with another differing by a <BRST-exact operator>. Since $s^2=0$, every exact operator is closed but represents the zero class. Thus closure by itself does not guarantee an independent physical observable; the <ghost number>, quotient by exact operators and the appropriate quantum consistency conditions also matter. A <gauge-invariant operator> provides the basic motivating example in an anomaly-free <gauge theory>.
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