Dissipation in quantum gases in the Keldysh-Schwinger formalism

We will talk about the calculation of the dissipation in the spectrum of equilibrium Bose and Fermi gases with weak local interaction. Using the Keldysh -Schwinger method, the spectrum was analyzed in the second order of perturbation theory. It is shown that the field-theoretic cause of the dissipation is associated with the divergences of Feynman diagrams at large times (pinch singularities). Such divergences can be eliminated by a specific method of “dressing” the regularization parameter using the Dyson-Schwinger equations, where the “dressing” parameter will be the dissipation parameter. The main result is the reduction of the problem to an extremely nontrivial asymptotic analysis of a certain class of integrals. The talk is based on joint work with Mikhail Nalimov, arXiv:2210.14281.