Confinement in the Coulomb Gauge Model

The Coulomb gauge model of QCD is studied with the introduction of a confining potential into the scalar part of the vector potential. Using a Green function formalism, we derive the self-energy for this model, which has both scalar and vector parts, $\Sigma^S(p)$ and $\Sigma^V(p)$. A rotation of these variables leads to the so-called gap and energy equations. We then analyse the divergence structure of these equations. As this depends explicitly on the form of potential, we give as examples both the linear plus Coulomb and quadratically confining potentials. The nature of the confining single particle Green function is investigated, and shown to be divergent due to the infrared singularities caused by the confining potential. Solutions to the gap equation for the simpler case of quadratic confinement are found both semi-analytically and numerically. At finite temperatures, the coupled set of equations are solved numerically in two decoupling approximations. Although chiral symmetry is found only to be exactly restored as $T\to\infty$, the chiral condensate displays a steep drop over a somewhat small temperature range.Comment: 31 pages Revtex, 2 PS files containing 11 figures, accepted for publication in Annals Of Physics (NY

Relativistic Transport Approach for Nucleus-Nucleus Collisions from SIS to SPS Energies

We formulate a covariant transport approach for high energy nucleus-nucleus collisions where the real part of the nucleon selfenergies is fitted to nuclear matter properties which are evaluated on the basis of a NJL-type Lagrangian for the quark degrees of freedom. The parameters of the quark-model Lagrangian are fixed by the Gell-Mann, Oakes and Renner relation, the pion- nucleon $\Sigma$-term, the nucleon energy as well as the nuclear binding energy at saturation density $\rho_0$. We find the resulting scalar and vector selfenergies for nucleons to be well in line with either Dirac-Brueckner computations for $\rho \leq 2 \rho_0$ or those from the phenomenological optical potential when accounting for a swelling of the nucleon at finite nuclear matter density. The meson-baryon interaction density is modelled to describe a decrease of the meson mass with baryon density. The imaginary part of the hadron selfenergies is determined by a string fragmentation model which accounts for the in-medium mass of hadrons in line with the 'chiral' dynamics employed. The applicability of the transport approach is demonstrated in comparison with experimental data from SIS to SPS energies. The enhancement of the K$^+/\pi^+$ ratio in A + A collisions compared to p + A reactions at AGS energies is reproduced within the 'chiral' dynamics. Furthermore, detailed predictions for the stopping in Pb + Pb collisions at 153 GeV/A are presented.Comment: 1 compressed uuencoded postscript file with 23 figures included, 45 page