Renormalized Linear Kinetic Theory as Derived from Quantum Field Theory - a novel diagrammatic method for computing transport coefficients -

We propose a novel diagrammatic method for computing transport coefficients in relativistic quantum field theory. The self-consistent equation for summing the diagrams with pinch singularities has a form of a linearized kinetic equation as usual, but our formalism enables us to incorporate higher-order corrections of the coupling systematically for the first time. Furthermore, it is clarified that the higher-order corrections are nicely summarized into that of the vertex function, spectral function, and collision term. We identify the diagrams up to the next-to-next-leading order corrections in the weak coupling expansion of phi^4 theory, which is a difficult task in kinetic approaches and other diagrammatic methods.