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A semiphenomenological transport theory of the quark-gluon plasma is formulated by means of an operator-field Langevin equation, which provides an intermediate step to transfer first principles to phenomenology. We first consider a damped quantum oscillator obeying an operator-valued Langevin equation and a generalized Nyquist theorem, whose input is designed to contain basic information about QCD matter such as a phase transition. The quantum property is reflected in the non-Markoffian character of the operator-valued stochastic process. A thermal field operator is then composed of such damped quantum oscillators, which is expected not only to describe the quark-gluon plasma or similar critical phenomena but also to have a close relation to the basic field theory. Using the thermal field operators, we formulate a transport theory to give theoretical formulas of thermodynamical quantities and transport coefficients explicitly written in terms of the above input. Their temperature dependences around a critical temperature are discussed for a few phenomenological models of phase transition.

Transport theory of the quark-gluon plasma based on an operator-field Langevin equation