= Worldline gauge-orbit determinant
{title2=$\Delta_{\mathrm{FP}}=\det{}^{\prime}\partial_t$}
On a unit interval with gauge parameters vanishing at its ends, $e=s+\dot\epsilon$ separates the <worldline einbein> into its invariant average $s$ and a <canonical gauge transformation>. The Jacobian for nonconstant modes is $\det\partial_t$ between the appropriate boundary-condition spaces. On a circle its prime excludes the constant gauge-parameter zero mode. This <Faddeev-Popov determinant> can be represented by anticommuting $b,c$ fields with an action proportional to $\int b\dot c\,dt$.
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