Nonequilibrium quantum meson gas: Dimensional reduction

Abstract

A nonequilibrium quantum gas of interacting relativistic effective mesons, ressembling qualitatively those produced in a heavy-ion collision, is described by a scalar \( \phi^{{4}}_{}\) quantum field in (1 + 3) -dimensional Minkowski space. For high temperature and large temporal and spatial scales, we justify that classical statistical mechanics including quantum renormalization effects describe approximately the gas: nonequilibrium dimensional reduction (NEDR). As a source of hints, we treat the gas at equilibrium in real-time formalism and obtain simplifications for high temperature and large spatial scales, thereby extending a useful equilibrium dimensional reduction known for the imaginary-time formalism. By assumption, the nonequilibrium initial state of the gas, not far from thermal equilibrium, includes interactions and inhomogeneities. We use nonequilibrium real-time generating functionals and correlators at nonzero temperature. In the NEDR regime, our arguments yield: 1) renormalized correlators simplify, 2) the perturbative series for those simplified correlators can be resummed into a new nonequilibrium generating functional, Z’r, dr , which is super-renormalizable and includes renormalization effects (large position-dependent thermal self-energies and effective couplings). Z’r, dr could enable to study nonperturbatively changes in the phase structures of the field, by proceeding from the nonequilibrium quantum regime to the NEDR one.