Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
1998-06-23
Nucl.Phys.B542:719-741,1999
Physics
High Energy Physics
High Energy Physics - Phenomenology
19 pages, 2 figures. Ref.s added, misprint fixed
Scientific paper
10.1016/S0550-3213(98)00804-9
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 U_k that incorporates the effect of fluctuations with characteristic momenta above a given scale k. U_k 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 S_k of this saddle point. The pre-exponential factor A_k, which includes the fluctuation determinant around the saddle-point configuration, is well-defined and finite. Both S_k and A_k 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.
Strumia Alessandro
Tetradis Nikolaos
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