Hydrodynamic Transport Coefficients in Relativistic Scalar Field Theory.

Convenient Cutkosky-like diagrammatic rules for computing the spectral densities of arbitrary two-point correlation functions in finite temperature field theory are derived. The approach is based on all explicit analytic continuation of imaginary-time Feynman diagrams and avoids the complications of real-time finite temperature perturbation theory. Hydrodynamic transport coefficients may be evaluated from first principles in a weakly coupled scalar field theory at arbitrary temperature. In a theory with cubic and quartic interactions, the infinite class of diagrams which contribute to the leading weak coupling behavior are identified and summed. The resulting expression is reduced to a single linear integral equation, which is shown to be identical to the corresponding result obtained from a linearized Boltzmann equation describing effective thermal excitations with temperature dependent masses and scattering amplitudes. The effective Boltzmann equation is valid even at very high temperature where the thermal lifetime and mean free path are short compared to the Compton wavelength of the fundamental particles.