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.
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Alvarez-Estrada, R.F. Nonequilibrium quantum meson gas: Dimensional reduction. Eur. Phys. J. A 41, 53–70 (2009). https://doi.org/10.1140/epja/i2009-10785-6
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DOI: https://doi.org/10.1140/epja/i2009-10785-6