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Nonequilibrium themal QFT

Wick rotation to thermal of QFT in Minkowski space to thermal QFT, which is after this transformation analogue to statistical mechanics, does only describe equilibrium statistical mechanics. On page ...
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Deriving the Sommerfeld expansion by contour integration (Le Bellac p. 277)

In Le Bellac's statistical physics book he derives the Sommerfeld expansion by a contour integral. The idea is to expand integrals of the type $I(\beta)\equiv \int_{0}^{\infty}d\epsilon\, ...