Basics of Thermal Field Theory pp 113-129 | Cite as

# Low-Energy Effective Field Theories

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## Abstract

The existence of a so-called infrared (IR) problem in relativistic thermal field theory is pointed out, both from a physical and a formal (imaginary-time) point of view. The notion of effective field theories is introduced, and the main issues related to their construction and use are illustrated with the help of a simple example. Subsequently this methodology is applied to the imaginary-time path integral representation for the partition function of non-Abelian gauge field theory. This leads to the construction of a dimensionally reduced effective field theory for capturing certain (so-called “static”, i.e. time-independent) properties of QCD (or more generally Standard Model) thermodynamics in the high-temperature limit.

## Keywords

Bose enhancement Effective theories Electrostatic QCD Hard and soft modes Infrared divergences Linde problem Magnetostatic QCD Matching Matsubara zero mode Power counting Symmetries Truncation## References

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