A quantum gas of interacting relativistic effective massive mesons at finite temperature (either at approximate thermal equilibrium or off-equilibrium), ressembling qualitatively those produced in a heavy-ion collision, is described by a scalar renormalizable relativistic quantum field theory (RRQFT) with quartic self-interaction, in (1+3)-dimensional Minkowski space.
A short discussion of the gas at equilibrium, in both imaginary and real time formalisms, is presented. Simplified descriptions of the equilibrium gas for high temperature and large spatial scales (equilibrium dimensional reduction or EDR) in both formalisms are summarized. In so doing, the well known (and certainly useful) EDR for the imaginary-time formalism is extended to the real-time one.
Most of the talk will be devoted to the off-equilibrium gas. A very short overview of existing approaches to the description of the time evolution of the off-equilibrium gas by other authors will be presented.
A general initial nonequilibrium state AT FINITE TIME in RRQFT gives rise to additional ultraviolet divergences, which pose known ( and harder) conceptual difficulties. In spite of the above general difficulties, for gases and plasmas described by effective RRQFT, there do exist restricted ( still physically meaningful) classes of initial nonequilibrium states for which the time evolutions do not meet those conceptual difficulties. Then, the time evolutions of the off-equilibrium gas can indeed be dealt with within the conceptual framework of perturbative renormalization, up to certain (non-trivial) modifications.
By assumption, the initial state AT FINITE TIME of the gas of effective mesons, not far from thermal equilibrium, belongs to the latter restricted class of initial nonequilibrium states and includes interactions and inhomogeneities. The gas at equilibrium in real-time formalism, outlined above, turns out to provide a source of hints for the off-equilibrium analysis. The time evolution of the off-equilibrium gas is described by means of nonequilibrium real-time generating functionals and correlators at non-zero temperature.
Main result.- For high temperature and large temporal and spatial scales, we justify that classical nonequilibrium statistical mechanics ( including crucial renormalization effects, remnants of the underlying quentum theory) do describe
approximately the gas: nonequilibrium dimensional reduction (NEDR). In the NEDR regime, our arguments yield: 1) renormalized correlators do simplify, 2) the perturbative series for those simplified correlators can be resummed into a nonequilibrium generating functional, which is super-renormalizable and includes renormalization effects (large position-dependent thermal self-energies and effective couplings). The latter super-renormalizable nonequilibrium generating functional for the NEDR regime could enable to study nonperturbatively changes in the phase structures of the field, by proceeding from a general nonequilibrium quantum regime to the NEDR one.
References: R. F. Alvarez-Estrada: 1) ``Initial States and Time Evolution in Nonequilibrium Quantum Field Theory'', Nucl. Phys. A, Vol. 785, 218c (2007); 2) Nonequilibrium Quantum Anharmonic Oscillator and Scalar Field: High Temperature Approximations, Ann. Phys. (Berlin), Vol. 18, 391 (2009); 3) Nonequilibrium Quantum Meson Gas: Dimensional Reduction, Eur. Phys. J. A, Vol. 41, 53 (2009).