= Instanton translation zero mode
{title2=$L_I\dot q_I=0$}
Differentiating the Euclidean classical equation for an <instanton> gives a zero eigenfunction proportional to its time derivative. Its norm satisfies $\mu\int\dot q_I^2d\tau=S_I$, so replacing the Gaussian zero-mode integral by the center coordinate gives $\sqrt{S_I/(2\pi\hbar)}d\tau_0$. The nonzero modes belong in the primed <functional determinant>. This removes the false divergence without deleting the center's integration volume.
Back to article page
