Heavy ion collisions: puzzles and hopes

This talk is a brief summary of some theoretical issues in the field of hot and dense QCD matter and ultra-relativistic heavy ion collisions.Comment: 6 pages, invited talk presented at the conference "Physics at the LHC 2010", DESY, June 7-12, 2010 Minor corrections in reference

Theoretical Conference Summary

This talk reviews progress reported at Quark-Matter 2001 on various theoretical aspects of the quark-gluon plasma and discusses how the new results obtained at RHIC change the standard picture of ultrarelativistic nucleus-nucleus collisions.Comment: Theoretical summary of the 15th International Conference on Ultrarelativistic Nucleus-Nucleus Collisions (Quark Matter 2001), Stony-Brook, NY, Jan. 15-20, 200

A Boltzmann Equation for the QCD Plasma

We present a derivation of a Boltzmann equation for the QCD plasma, starting from the quantum field equations. The derivation is based on a gauge covariant gradient expansion which takes consistently into account all possible dependences on the gauge coupling assumed to be small. We point out a limitation of the gradient expansion arising when the range of the interactions becomes comparable with that of the space-time inhomogeneities of the system. The method is first applied to the case of scalar electrodynamics, and then to the description of long wavelength colour fluctuations in the QCD plasma. In the latter case, we recover B\"odeker's effective theory and its recent reformulation by Arnold, Son and Yaffe. We discuss interesting cancellations among various collision terms, which occur in the calculation of most transport coefficients, but not in that of the quasiparticle lifetime, or in that of the relaxation time of colour excitations.Comment: 58 pages, 11 figures, LaTeX, some references added, new abstract. Final version, as published in Nucl.Phys.

The Quark-Gluon Plasma: Collective Dynamics and Hard Thermal Loops

We present a unified description of the high temperature phase of QCD, the so-called quark-gluon plasma, in a regime where the effective gauge coupling $g$ is sufficiently small to allow for weak coupling calculations. The main focuss is the construction of the effective theory for the collective excitations which develop at a typical scale $gT$, which is well separated from the typical energy of single particle excitations which is the temperature $T$. We show that the plasma particles provide a source for long wavelength oscillations of average fields which carry the quantum numbers of the plasma constituents, the quarks and the gluons. To leading order in $g$, the plasma particles obey simple gauge-covariant kinetic equations, whose derivation from the general Dyson-Schwinger equations is outlined. As a by-product, the ``hard thermal loops'' emerge naturally in a physically transparent framework. We show that the collective excitations can be described in terms of classical fields, and develop for these a Hamiltonian formalism. The effect of collisions among the hard particles is also studied, in particular in relation with the effective theory for ultrasoft excitations, with momenta $\sim g^2T$.Comment: 210 pages, 33 figures, submitted to Physics Report