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.

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