Juha Honkonen: Generating functionals for time-dependent Green functions at finite temperature

Quantum kinetic theory may be constructed with the use of statistical expectation values of products of Heisenberg field operators. In the grand canonical ensemble this gives rise to time-dependent Green functions at finite temperature (TDGF@T). Perturbation theory for the generating functional of full TDGF@T’s is constructed with the aid of functional-differential representation for Wick’s theorems for time-ordered products. It is pointed out that the transformation of products of operators in the Heisenberg picture into products operators in the Dirac picture is generic and applicable to construction of generating functions of correlation functions in stochastic problems brought about by classical kinetic theory as well. It is shown that quantum kinetic theory and classical stochastic problems differ by the method of calculation of expectation values. Specific problems of translation of the functional-differential representation of the generating functional of full TDGF@T’s into a functional integral are reviewed. Unusual divergences of the perturbation expansion are pointed as well as the renormalization of TDGF@T’s. The role of dissipation in the construction of regularized perturbation theory in the wave-vector space is discussed.

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