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Juha Honkonen: *Critical behaviour of time-dependent Green functions of boson gas from renormalization group*

Construction of quantum kinetic theory with the use of statistical expectation values of products of Heisenberg field operators is reviewed. In the grand canonical ensemble this gives rise to time-dependent Green functions at finite temperature (GF@FT). Perturbation theory for the generating functional of full GF@FT’s is constructed with the aid of functional-differential representation for Wick’s theorems for time-ordered products. Ambiguities of translation of the functional-differential representation of the generating functional of full GF@FT’s into a functional integral are discussed. Unusual divergences of the perturbation expansion are pointed out and a regularized field theory with unambiguous functional-integral representation put forward. An effective large-scale model is inferred with the use of scaling analysis and the renormalization group. A field-theoretic renormalization-group analysis of the effective model is carried out and the dynamic critical exponents of the boson gas calculated at the leading non-trivial order. Effects of the two different thermodynamic limits (box and oscillator potential) are discussed.