A precise computation of a vacuum decay rate requires the determination of the prefactor in front of the exponential suppression factor. When the decay is driven by charged scalar field(s), the prefactor includes the functional determinants of the gauge boson and the Faddeev-Popov fluctuation operators. They depend on the gauge fixing parameter non-trivially and it has not been clear how this dependence cancels out in the final results. We have explicitly proven that the functional determinants become independent of the gauge parameter for a general setup with multiple scalar and gauge fields. 

The subtraction of the gauge zero modes is necessary to make the functional determinant finite. The path integral over these zero modes is translated into an integration over the collective coordinates, requiring a Jacobian. Due to the gauge fixing terms, the Jacobian becomes non-trivial and gauge-dependent. We have determined the correct Jacobian, which makes it possible to calculate the prefactor for general scalar and gauge fields.