where the short-hand notation is used. The operator may be interpreted as a

Therefore, the single-particle GREEN's function at finite temperature can be defined as

At this stage, this form of the GREEN's function does not admit the WICK decomposition, because the WICK theorem described in Section 3.4.1 requires a dependence on the non-interacting HAMILTONian for both the field operators and the thermal average. A way around this problem is the MATSUBARA technique [193], where one introduces a complex time and a new physical quantity, the MATSUBARA (imaginary time) GREEN's function . The representation of operators with imaginary time arguments is given in Appendix B.5.