Thermal EFT, Screening, and Resummation
A weak microscopic coupling does not guarantee a uniform thermal expansion. Effective field theory separates hard and soft modes, while resummation incorporates enhanced contributions without counting them twice.
Enter this chapter
Section titled “Enter this chapter”Begin with Thermal Modes, Matching, and EFT Power Counting to choose retained modes from the observable and desired accuracy.
Helpful background. Thermal Modes, Matching, and EFT Power Counting and Scale Separation, Locality, and the Domain of an EFT develop the definitions used by the chapter’s opening pages.
Topics
Section titled “Topics”- Thermal Modes, Matching, and EFT Power Counting — Turns an observable and accuracy goal into a mode inventory, operator basis, and matching calculation.
- Screening and Infrared Scale Separation — Distinguishes scalar, electric, magnetic, and dynamical screening.
- Ring and Daisy Resummation — Derives the leading static determinant and its double-counting subtraction.
- Screened and Variational Thermal Expansions — Explains add–subtract reorganizations and why auxiliary parameters remain prescription-dependent.
- Dimensional Reduction and Static Effective Theories — Constructs a local three-dimensional description of static long-distance observables.
- Real-Time Thermal EFT and Dissipative Matching — Separately matches causal response, fluctuations, and memory.
- Double Counting, Matching Dependence, and Breakdown — Supplies the final falsification tests.
How the ideas fit together
Section titled “How the ideas fit together”Matching fixes the coefficients of a theory for the retained modes by comparing common observables. The hard matching calculation can be perturbative even when the resulting soft theory is strongly coupled. This is why high-temperature dimensional reduction organizes a problem without necessarily solving its longest-distance sector Laine and Vuorinen 2016, chs. 5–6.
Static dimensional reduction matches zero-frequency Euclidean quantities. A damping rate or noise kernel instead requires real-time response and fluctuation information. Neither a static screening mass nor successful pressure matching supplies that missing dynamical information.
Where to go next
Section titled “Where to go next”Continue to Thermal Phases, Metastability, and Nucleation to describe phases and interfaces with a coarse-grained free-energy functional.
References
Section titled “References”- Laine, Mikko, and Aleksi Vuorinen. Basics of Thermal Field Theory: A Tutorial on Perturbative Computations. Lecture Notes in Physics 925. Cham: Springer, 2016. doi:10.1007/978-3-319-31933-9.