nLab infinite-temperature thermal field theory



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Broadly speaking, high- or infinite-temperature thermal field theory is thermal field theory in or around the limiting case of very high or (practically) infinite temperature TT.

This is relevant for example in the study of extreme phases of matter such as the quark-gluon plasma of QCD (Blaizot-Iancu-Rebhan 03, section 2.2.4, Blaizot 04, around p. 17).

More concretely, with the formulation of thermal field theory via Wick rotation as a Euclidean field theory on a Riemannian manifold X 3×S β 1X_3 \times S^1_\beta whose compact/periodic Euclidean time runs along a circle S β 1S^1_\beta of circumference the inverse temperature β=1/T\beta = 1/T, the limit of infinite temperature corresponds to the limit β0\beta \to 0 in which this circle fiber shrinks away.

In terms of the thermal Euclidean field theory on X 3×S β 1X_3 \times S^1_\beta therefore the infinite-temperature limit is given by Kaluaza-Klein-type dimensional reduction along this circle fiber to a 3-dimensional Euclidean field theory on X 3X_3 (Ginsparg 80, Appelquist-Pisarski 81, Nadkarni 83, Jourjine 84, Nadkarni 88).

As usual with KK-reduction, some care must be exercised to ensure that the compactified theory is itself still a local field theory. Depending on how exactly one proceeds this may be subtle (Landsman 89), but there exist robust approaches (Reisz 92, Kajantie-Laine-Rummukainen-Shaposhnikov 96).


The expansion of thermal field theory around the infinite-temperature-limit (i.e. around β=1/T=0\beta = 1/T = 0, i.e. KK-reduction in compact/periodic Euclidean time) is discussed in

and specifically with an eye to discussion of the quark-gluon plasma in

  • Jean-Paul Blaizot, Edmond Iancu, Anton Rebhan, section 2.2.4 of Thermodynamics of the high temperature quark gluon plasma, Quark–Gluon Plasma 3, pp. 60-122 (2004) (arXiv:hep-ph/0303185, spire:615570)

  • Jean-Paul Blaizot, around p. 17 of Thermodynamics of the high temperature Quark-Gluon Plasma, AIP Conf. Proc. 739, 63-96 (2004) (doi:10.1063/1.1843592)

Last revised on December 8, 2022 at 07:33:00. See the history of this page for a list of all contributions to it.