Off-shell effects on particle production

We investigate the observable effects of off-shell propagation of nucleons in heavy-ion collisions at SIS energies. Within a semi-classical BUU transport model we find a strong enhancement of subthreshold particle production when off-shell nucleons are propagated.Comment: 11 pages, 3 figure

Particle production in quantum transport theories

The particle production in the intermediate energy heavy ion collisions is discussed in the framework of the nonequilibrium Green's functions formalism. The evolution equations of the Green's functions for fermions allows for the discussion of the off-shell fermion propagator and of the large momentum component in the initial state. For the case of a homogeneous system numerical calculations of the meson production rate are performed and compared with the semiclassical production rate.Comment: 45 pages, figures included, uses FEYNMAN macro

Equilibration within a semiclassical off-shell transport approach

Equilibration times for nuclear matter configurations -- modelling intermediate and high energy nucleus-nucleus collisions -- are evaluated within the semiclassical off-shell transport approach developed recently. The transport equations are solved for a finite box in coordinate space employing periodic boundary conditions. The off-shell transport model is shown to give proper off-shell equilibrium distributions in the limit $t \to \infty$ for the nucleon and $\Delta$-resonance spectral functions. We find that equilibration times within the off-shell approach are only slightly enhanced as compared to the on-shell limit for the momentum configurations considered.Comment: 19 pages, LaTeX, including 4 postscript figures, submitted to Nucl. Phys.

Correlations and Equilibration in Relativistic Quantum Systems

In this article we study the time evolution of an interacting field theoretical system, i.e. \phi^4-field theory in 2+1 space-time dimensions, on the basis of the Kadanoff-Baym equations for a spatially homogeneous system including the self-consistent tadpole and sunset self-energies. We find that equilibration is achieved only by inclusion of the sunset self-energy. Simultaneously, the time evolution of the scalar particle spectral function is studied for various initial states. We also compare associated solutions of the corresponding Boltzmann equation to the full Kadanoff-Baym theory. This comparison shows that a consistent inclusion of the spectral function has a significant impact on the equilibration rates only if the width of the spectral function becomes larger than 1/3 of the particle mass. Furthermore, based on these findings, the conventional transport of particles in the on-shell quasiparticle limit is extended to particles of finite life time by means of a dynamical spectral function A(X,\vec{p},M^2). The off-shell propagation is implemented in the Hadron-String-Dynamics (HSD) transport code and applied to the dynamics of nucleus-nucleus collisions.Comment: 20 pages, 7 figures to appear in "Nonequilibrium at short time scales - Formation of correlations", edited by K. Morawetz, Springer, Berlin (2003), p16

Baryon flow at SIS energies

We calculate the baryon flow $$ in the energy range from .25 to $\le 2.5 AGeV$ in a relativistic transport model for $Ni+Ni$ and $Au+Au$ collisions employing various models for the baryon self energies. We find that to describe the flow data of the FOPI Collaboration the strength of the vector potential has to be reduced at high relative momentum or at high density such that the Schr\"odinger- equivalent potential at normal nuclear density decreases above 1 GeV relative kinetic energy and approaches zero above 2 GeV.Comment: 20 pages, LATEX, 7 PostScript figure

Towards a fully self-consistent spectral function of the nucleon in nuclear matter

We present a calculation of nuclear matter which goes beyond the usual quasi-particle approximation in that it includes part of the off-shell dependence of the self-energy in the self-consistent solution of the single-particle spectrum. The spectral function is separated in contributions for energies above and below the chemical potential. For holes we approximate the spectral function for energies below the chemical potential by a $\delta$-function at the quasi-particle peak and retain the standard form for energies above the chemical potential. For particles a similar procedure is followed. The approximated spectral function is consistently used at all levels of the calculation. Results for a model calculation are presented, the main conclusion is that although several observables are affected by the inclusion of the continuum contributions the physical consistency of the model does not improve with the improved self-consistency of the solution method. This in contrast to expectations based on the crucial role of self-consistency in the proofs of conservation laws.Comment: 26 pages Revtex with 4 figures, submitted to Phys. Rev.

Spectral Function of Quarks in Quark Matter

We investigate the spectral function of light quarks in infinite quark matter using a simple, albeit self-consistent model. The interactions between the quarks are described by the SU(2) Nambu--Jona-Lasinio model. Currently mean field effects are neglected and all calculations are performed in the chirally restored phase at zero temperature. Relations between correlation functions and collision rates are used to calculate the spectral function in an iterative process.Comment: final version, published in PRC; 15 pages, RevTeX

Space-time versus particle-hole symmetry in quantum Enskog equations

The non-local scattering-in and -out integrals of the Enskog equation have reversed displacements of colliding particles reflecting that the -in and -out processes are conjugated by the space and time inversions. Generalisations of the Enskog equation to Fermi liquid systems are hindered by a request of the particle-hole symmetry which contradicts the reversed displacements. We resolve this problem with the help of the optical theorem. It is found that space-time and particle-hole symmetry can only be fulfilled simultaneously for the Bruckner-type of internal Pauli-blocking while the Feynman-Galitskii form allows only for particle-hole symmetry but not for space-time symmetry due to a stimulated emission of Bosons

Generalized Boltzmann Equation in a Manifestly Covariant Relativistic Statistical Mechanics

We consider the relativistic statistical mechanics of an ensemble of $N$ events with motion in space-time parametrized by an invariant ``historical time'' $\tau .$ We generalize the approach of Yang and Yao, based on the Wigner distribution functions and the Bogoliubov hypotheses, to find the approximate dynamical equation for the kinetic state of any nonequilibrium system to the relativistic case, and obtain a manifestly covariant Boltzmann-type equation which is a relativistic generalization of the Boltzmann-Uehling-Uhlenbeck (BUU) equation for indistinguishable particles. This equation is then used to prove the $H$-theorem for evolution in $\tau .$ In the equilibrium limit, the covariant forms of the standard statistical mechanical distributions are obtained. We introduce two-body interactions by means of the direct action potential $V(q),$ where $q$ is an invariant distance in the Minkowski space-time. The two-body correlations are taken to have the support in a relative $O( 2,1)$-invariant subregion of the full spacelike region. The expressions for the energy density and pressure are obtained and shown to have the same forms (in terms of an invariant distance parameter) as those of the nonrelativistic theory and to provide the correct nonrelativistic limit

Chiral symmetry breaking in hot matter

This series of three lectures covers (a) a basic introduction to symmetry breaking in general and chiral symmetry breaking in QCD, (b) an overview of the present status of lattice data and the knowlegde that we have at finite temperature from chiral perturbation theory. (c) Results obtained from the Nambu--Jona-Lasinio model describing static mesonic properties are discussed as well as the bulk thermodynamic quantities. Divergences that are observed in the elastic quark-antiquark scattering cross-section, reminiscent of the phenomenon of critical opalescence in light scattering, is also discussed. (d) Finally, we deal with the realm of systems out of equilibrium, and examine the effects of a medium dependent condensate in a system of interacting quarks.Comment: 62 LaTex pages, incorporating 23 figures. Lectures given at the eleventh Chris-Engelbrecht Summer School in Theoretical Physics, 4-13 February, 1998, to be published by Springer Verla