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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeNov 8th 2018

am finally adding references here, such as

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

• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeNov 8th 2018

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

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeNov 8th 2018
• (edited Nov 8th 2018)

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)
• CommentRowNumber4.
• CommentAuthorUrs
• CommentTimeNov 9th 2018

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

• CommentRowNumber5.
• CommentAuthorUrs
• CommentTimeNov 9th 2018

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

• CommentRowNumber6.
• CommentAuthorUrs
• CommentTimeNov 16th 2018
• (edited Nov 16th 2018)

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)
• CommentRowNumber7.
• CommentAuthorUrs
• CommentTimeNov 16th 2018

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