Fluctuations about the Fubini-Lipatov instanton for false vacuum decay in classically scale invariant models

For a scalar theory whose classical scale invariance is broken by quantum effects, we compute self-consistent bounce solutions and Green's functions. Deriving analytic expressions, we find that the latter are similar to the Green's functions in the archetypal thin-wall model for tunneling between quasi-degenerate vacua. The eigenmodes and eigenspectra are, however, very different. Large infrared effects from the modes of low angular momentum $j=0$ and $j=1$, which include the approximate dilatational modes for $j=0$, are dealt with by a resummation of one-loop effects. For a parametric example, this resummation is carried out numerically.