“Matsubara formalism” should probably redirect to “thermal quantum field theory”, once that entry exists, if that’s what you mean.

]]>Urs ad 2:

Once you have time could you briefly hint what did you mean about splitting off thermal quantum field theory and Matsubara formalism. I agree about the need for separate entries but I am confused with implied. I mean the present version of the page is such that more than half of the references and material is anyway about thermal field theory and the discussion also equates the notion with Matsubara formalism. The equality is however not true (probably not intended) as the real time thermal field theory also exists, for example there is the Keldysh-Schwinger formalism which is real time (though it uses tricks with paths in complex plane). The wikipedia page thermal quantum field theory clearly delimits the imaginary and real time approaches. For a practitioner, Matsubara formalism is typically easier to compute with than the real time approaches. Also if the thermal field theory is split, what should stay in the original page duplicated ?

]]>added two more reference on the perturbation around the infinite-temperature limit:

Klaas Landsman,

*Limitations to dimensional reduction at high temperature*, Nuclear Physics B Volume 322, Issue 2, 14 August 1989, Pages 498-530 (doi:10.1016/0550-3213(89)90424-0)T. Reisz,

*Realization of dimensional reduction at high temperature*, Z. Phys. C - Particles and Fields (1992) 53: 169 (doi:10.1007/BF01483886)

added the following pointer:

The perturbative expansion of thermal field theory around the infinite-temperature-limit (i.e. around $\beta = 1/T = 0$) is discussed in

- Alexander N Jourjine,
*Quantum field theory in the infinite temperature limit*, Annals of Physics Volume 155, Issue 2, July 1984, Pages 305-332 (doi:10.1016/0003-4916(84)90003-4)

added to the section “Idea – General” mentioning of more classes of examples (CFTs and diffeomorphism-gauge fixed TQFTs) as well as mentioning of formulation in terms of configuration spaces

]]>further exanded the Idea-section a fair bit and added more references, such as on literature explicitly discussing the Osterwalder-Schrader theorem for compact Euclidean time:

- Abel Klein, Lawrence Landau,
*Periodic Gaussian Osterwalder-Schrader positive processes and the two-sided Markov property on the circle*, Pacific Journal of Mathematics, Vol. 94, No. 2, 1981 ( DOI: 10.2140/pjm.1981.94.341, pdf)

Will copy relvant bits also to the entries *Wick rotation* and *Osterwalder-Schrader theorem*

added further pointers regarding thermal field theory as time-periodic Euclidean field theory. Of the many reviews, this one here stands out in clarity, coherence and scope:

- S.A. Fulling, S.N.M. Ruijsenaars,
*Temperature, periodicity and horizons*, Physics Reports Volume 152, Issue 3, August 1987, Pages 135-176 (pdf, doi:10.1016/0370-1573(87)90136-0)

added bried paragraph on relation to thermal quantum field theory and “compact periodic Euclidean time”, added some more references. But of course it remains a stub.

made, for the moment, various keywords redirect here, which should eventually be split off as entries in their own right: *thermal quantum field theory*, *Matsubara formalism*, *KMS condition*

am finally adding references here, such as

- Kasper Peeters, Marija Zamaklar,
*Euclidean Field Theory*, Lecture notes 2009-2011 (web, pdf)

will add these also to *lattice gauge theory* as far as there is overlap