A consistent calculation of bubble-nucleation rates Original Research Article

We present a consistent picture of tunnelling in field theory. Our results apply both to high-temperature field theories in four dimensions and to zero-temperature three-dimensional ones. Our approach is based on the notion of a coarse-grained potential Uk that incorporates the effect of fluctuations with characteristic momenta above a given scale k. Uk is non-convex and becomes equal to the convex effective potential for k → 0. We demonstrate that a consistent calculation of the nucleation rate must be performed at non-zero values of k, larger than the typical scale of the saddle-point configuration that dominates tunnelling. The nucleation rate is exponentially suppressed by the action Sk of this saddle point. The pre-exponential factor Ak, which includes the fluctuation determinant around the saddle-point configuration, is well-defined and finite. Both Sk and Ak are k-dependent, but this dependence cancels in the expression for the nucleation rate. This picture breaks down in the limit of very weakly first-order phase transitions, for which the pre-exponential factor compensates the exponential suppression.