标题： 气泡核化的稳定计算速率 显示英文标题

标题： A Consistent Calculation of Bubble-Nucleation Rates

摘要： 我们提出了场论中隧穿现象的一致图景。 我们的结果既适用于四维高温场理论，也适用于零温三维场理论。 我们的方法基于一个粗粒化势能的概念 U_k，它包含了尺度 k 以上的特征动量涨落的影响。U_k 是非凸的，并且当 k 趋向于 0 时等于凸的有效势能。 我们证明了核化率的一致计算必须在非零的 k 值上进行，且大于主导隧穿的鞍点构型的典型尺度。 核化率被这个鞍点的作用量 S_k 指数抑制。 前指数因子 A_k，它包括了围绕鞍点构型的涨落行列式，是定义良好且有限的。 S_k 和 A_k 都依赖于 k，但这种依赖性在核化率的表达式中相互抵消。 对于非常弱的第一阶相变极限情况，这一图景失效，此时前指数因子补偿了指数抑制效应。 显示英文摘要

摘要： 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.