Basics of Thermal Field Theory by Mikko Laine & Aleksi Vuorinen

Author:Mikko Laine & Aleksi Vuorinen
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

(8.8)

which appear in time-dependent perturbation theory at zero temperature, or with the “Euclidean” correlator

(8.9)

which appears in non-perturbative formulations. Restricting to 0 ≤ τ ≤ β, the Euclidean correlator is also time-ordered, and can be computed with standard imaginary-time functional integrals. If the correlator is periodic [cf. text below Eq. (8.10)], then k n is a bosonic Matsubara frequency.

It follows from Eq. (8.1), by using the cyclicity of the trace, that

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