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Stop comparing resummation methods
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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.
Forward citations
Cited by 7 Pith papers
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Dynamics of nucleation in thermal phase transitions
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Thermal Resummation for Very Strong First-order Phase Transitions
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With renormalisation-group running included, the one-loop high-temperature Daisy-resummed potential at µ=πT reproduces the phase-transition parameters of the two-loop dimensionally reduced EFT, while the no-running on...
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