  We introduce a Green's function method for handling radiative effects on
false vacuum decay. In addition to the usual thin-wall approximation, we
achieve further simplification by treating the bubble wall in the planar limit.
As an application, we take the $\lambda\phi^4$ theory, extended with $N$
additional heavier scalars, wherein we calculate analytically both the
functional determinant of the quadratic fluctuations about the classical
soliton configuration and the first correction to the soliton configuration
itself.
