  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.
