Non Perturbative Renormalization Group, momentum dependence of nn-point functions and the transition temperature of the weakly interacting Bose gas

We propose a new approximation scheme to solve the Non Perturbative Renormalization Group equations and obtain the full momentum dependence of $n$-point functions. This scheme involves an iteration procedure built on an extension of the Local Potential Approximation commonly used within the Non Perturbative Renormalization Group. Perturbative and scaling regimes are accurately reproduced. The method is applied to the calculation of the shift $\Delta T_c$ in the transition temperature of the weakly repulsive Bose gas, a quantity which is very sensitive to all momenta intermediate between these two regions. The leading order result is in agreement with lattice calculations, albeit with a theoretical uncertainty of about 25%. The next-to-leading order differs by about 10% from the best accepted result

Stars and statistical physics: a teaching experience

The physics of stars, their workings and their evolution, is a goldmine of problems in statistical mechanics and thermodynamics. We discuss many examples that illustrate the possibility of deepening student's knowledge of statistical mechanics by an introductory study of stars. The matter constituting the various stellar objects provides examples of equations of state for classical or quantal and relativistic or non-relativistic gases. Maximum entropy can be used to characterize thermodynamic and gravitational equilibrium which determines the structure of stars and predicts their instability above a certain mass. Contraction accompanying radiation induces either heating or cooling, which explains the formation of stars above a minimum mass. The characteristics of the emitted light are understood from black-body radiation and more precisely from the Boltzmann-Lorentz kinetic equation for photons. The luminosity is governed by the transport of heat by photons from the center to the surface. Heat production by thermonuclear fusion is determined by microscopic balance equations. The stability of the steady state of stars is controlled by the interplay of thermodynamics and gravitation.Comment: latex gould_last.tex, 4 files, submitted to Am. J. Phy

DCC: Attractive Idea Seeks Serious Confirmation

The theoretical ideas relevant for the physics of the disoriented chiral condensate (DCC) are reviewed.Comment: 18 pages LaTex, based on invited lecture given by A.Krzywicki at the workshop "Quark, plasma and beyond", Zif, Bielefeld, May 1996 ; a reference is correcte

Confinement, Turbulence and Diffraction Catastrophes

Many features of large N_c transition that occurs in the spectral density of Wilson loops as a function of loop area (observed recently in numerical simulations of Yang-Mills theory by Narayanan and Neuberger) can be captured by a simple Burgers equation used to model turbulence. Spectral shock waves that precede this asymptotic limit exhibit universal scaling with N_c, with indices that can be related to Berry indices for diffraction catastrophes.Comment: Presented at PANIC 200

Comparing different hard-thermal-loop approaches to quark number susceptibilities

We compare our previously proposed hard-thermal-loop (HTL) resummed calculation of quark number susceptibilities using a self-consistent two-loop approximation to the quark density with a recent calculation of the same quantity at the one-loop level in a variant of HTL-screened perturbation theory. Besides pointing out conceptual problems with the latter approach, we show that it severely over-includes the leading-order interaction effects while including none of the plasmon term which after all is the reason to construct improved resummation schemes.Comment: 6 pages, 6 figures. Revised version to appear in Eur. J. Phys.

Proton-nucleus collisions in the color glass condensate framework

We discuss proton-nucleus collisions in the framework of the color glass condensate. By assuming that the proton can be described as a low density color source, we solve exactly the Yang-Mills equations corresponding to this type of collision, and then use this solution in order to calculate inclusive gluon production or quark-antiquark production. Our result shows that k_T-factorization, while valid for gluon production, is violated for quark pair production in proton-nucleus collisions.Comment: Talk given at SEWM2004, Helsinki, June 200

Thermodynamics of the high-temperature quark-gluon plasma

We review the various methods which have been employed recently to describe the thermodynamics of the high temperature quark-gluon plasma using weak coupling techniques, and we compare their results with those of most recent lattice gauge calculations. Many of the difficulties encountered with perturbation theory at finite temperature are in fact not specific to QCD but are present in any field theory at finite temperature and will be discussed first in the simple example of the scalar field theory. We discuss the merits and limitations of various techniques which have been used to go beyond perturbation theory in the soft sector, such as dimensional reduction, screened perturbation theory or hard-thermal-loop perturbation theory, and Phi-derivable approximations. In the last part of the review, we focus on the later, which lead to a remarkably simple expression for the entropy of the quark-gluon plasma. When complemented with further, physically motivated, approximations, this approach reproduces accurately the entropy obtained from lattice gauge calculations at temperatures above 2.5 T_c, where T_c is the deconfinement temperature. This calculation thus provides also support to the physical picture of the quark-gluon plasma as a gas of weakly interacting quasiparticles.Comment: Review for "Quark-Gluon Plasma 3", eds. R.C. Hwa and X.-N. Wang, World Scientific, Singapore. 63 pages, 21 figures. v2: minor corrections and 2 references adde

The thermodynamics of the quark-gluon plasma: Self-consistent resummations vs. lattice data

We discuss a recent approach for overcoming the poor convergence of the perturbative expansion for the thermodynamic potential of QCD. This approach is based on self-consistent approximations which allow for a gauge-invariant and manifestly ultraviolet-finite resummation of the essential physics of the hard thermal/dense loops. The results thus obtained are in good agreement with available lattice data down to temperatures of about twice the critical temperature. Calculations for a plasma with finite quark density (i.e., with a non-zero chemical potential $\mu$) are no more difficult than at $\mu=0$.Comment: 4 pages LaTeX2e, contribution to the proceedings of the 15th International Conference on Ultra-Relativistic Nucleus-Nucleus Collisions (QM 2001), Long Island, New York, January 15 - 20, 200