I argue that the consistency of any resummation method can be established if the method follows a power counting derived from a hierarchy of scales. I.e. whether it encodes a top-down effective field theory. This resolves much confusion over which resummation method to use once an approximation scheme is settled on. And if no hierarchy of scales exists, you should be wary about resumming. I give evidence from the study of phase transitions in thermal field theory, where adopting a consistent power-counting scheme and performing a strict perturbative expansion dissolves many common problems of such studies: gauge dependence, strong renormalization scale dependence, the Goldstone boson catastrophe, IR divergences, imaginary potentials, mirages (illusory barriers), perturbative breakdown, and linear terms.

中文翻译：

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停止比较恢复方法


我认为，如果任何恢复方法遵循从等级层次导出的幂计数，则可以建立该方法的一致性。 IE。它是否编码自上而下的有效场论。一旦确定了近似方案，这就解决了使用哪种恢复方法的许多困惑。如果不存在等级层次，你应该对重新开始保持警惕。我提供了热场理论中相变研究的证据，其中采用一致的功率计数方案并执行严格的微扰展开解决了此类研究的许多常见问题：规范依赖性、强重正化尺度依赖性、戈德斯通玻色子灾难、IR散度、虚势、海市蜃楼（虚幻障碍）、微扰分解和线性项。