Diagrammatical study of a nonequilibrium process: Model calculation

Quantum kinetic equation in the closed-time-path formalism

A systematic derivation of the quantum kinetic equation is presented in the framework of a closed-time-path formalism. Introducing a probe, the expectation value of the number operator is calculated as a functional of the probing source. Then, solving for the source by inverting the relation, the removal of the source leads to the quantum kinetic equation as the equation of motion for the number, which gives a generalization of the Boltzmann equation including memory. The inversion formula is used in the course of the derivation. The calculation is presented up to third order in interaction, and the effect of initial correlations is also considered.

Novel Use of Legendre Transformation in Field Theory and Many Particle Systems

The Legendre transformation is one of the ways to rewrite the theory by small number of selected variables. It leads naturally to the generalized action functional called the effective action and everything starts from this generating functional. It is applied to various problems of physics ranging from the relativistic field theory to the condensed matter physics. The main techniques used here are the on-shell expansion and the inversion method.

The scheme presented in this article is thus a generating functional formalism of the many particle systems.