2PI renormalized effective action for gauge theories

We show how to perform renormalization in the framework of the 2PI effective action for abelian gauge theories. In addition to the usual renormalization conditions one needs to incorporate new ones in order to remove non-transverse UV divergences in the truncated two- and four-photon functions. The corresponding counterterms are allowed by gauge symmetry, in-medium independent and suppressed with respect to the accuracy of the truncation.Comment: 4 pages, to appear in the proceedings of Strong and Electroweak Matter 2006, BNL, New-York, May 200

Progress in Nonequilibrium Quantum Field Theory

We review recent developments for the description of far-from-equilibrium dynamics of quantum fields and subsequent thermalization.Comment: To appear in the proceedings of Strong and Electroweak Matter (SEWM 2002), Heidelberg, Germany, 2-5 Oct 2002, 16 pages, 11 figure

Kinetic equilibration in heavy ion collisions: The role of elastic processes

We study the kinetic equilibration of gluons produced in the very early stages of a high energy heavy ion collision in a ``self-consistent'' relaxation time approximation. We compare two scenarios describing the initial state of the gluon system, namely the saturation and the minijet scenarios, both at RHIC and LHC energies. We argue that, in order to characterize kinetic equilibration, it is relevant to test the isotropy of various observables. As a consequence, we find in particular that in both scenarios elastic processes are not sufficient for the system to reach kinetic equilibrium at RHIC energies. More generally, we show that, contrary to what is often assumed in the literature, elastic collisions alone are not sufficient to rapidly achieve kinetic equilibration. Because of longitudinal expansion at early times, the actual equilibration time is at least of the order of a few fermis.Comment: 10 pages, 2 tables, 5 figures, references added, submitted to JHE

Parametric resonance in quantum field theory

We present the first study of parametric resonance in quantum field theory from a complete next-to-leading order calculation in a 1/N-expansion of the 2PI effective action, which includes scattering and memory effects. We present a complete numerical solution for an O(N)-symmetric scalar theory and provide an approximate analytic description of the nonlinear dynamics in the entire amplification range. We find that the classical resonant amplification at early times is followed by a collective amplification regime with explosive particle production in a broad momentum range, which is not accessible in a leading-order calculation.Comment: 4 pages, 5 figures, version to appear in Phys. Rev. Lett., results unchange

Quantum properties of a non-Gaussian state in the large-N approximation

We study the properties of a non-Gaussian density matrix for a O(N) scalar field in the context of the incomplete description picture. This is of relevance for studies of decoherence and entropy production in quantum field theory. In particular, we study how the inclusion of the simplest non-Gaussian correlator in the set of measured observables modifies the effective (Gaussian) description one can infer from the knowledge of the two-point functions only. We compute exactly the matrix elements of the non-Gaussian density matrix at leading order in a 1/N-expansion. This allows us to study the quantum properties (purity, entropy, coherence) of the corresponding state for arbitrarily strong nongaussianity. We find that if the Gaussian and the non-Gaussian observers essentially agree concerning quantum purity or correlation entropy, their conclusion can significantly differ for other, more detailed aspects such as the degree of quantum coherence of the system.Comment: 14 pages, 7 figures. Published version (Phys. Rev. D, minor corrections

Yang-Mills correlators across the deconfinement phase transition

We compute the finite temperature ghost and gluon propagators of Yang-Mills theory in the Landau-DeWitt gauge. The background field that enters the definition of the latter is intimately related with the (gauge-invariant) Polyakov loop and serves as an equivalent order parameter for the deconfinement transition. We use an effective gauge-fixed description where the nonperturbative infrared dynamics of the theory is parametrized by a gluon mass which, as argued elsewhere, may originate from the Gribov ambiguity. In this scheme, one can perform consistent perturbative calculations down to infrared momenta, which have been shown to correctly describe the phase diagram of Yang-Mills theories in four dimensions as well as the zero-temperature correlators computed in lattice simulations. In this article, we provide the one-loop expressions of the finite temperature Landau-DeWitt ghost and gluon propagators for a large class of gauge groups and present explicit results for the SU(2) case. These are substantially different from those previously obtained in the Landau gauge, which corresponds to a vanishing background field. The nonanalyticity of the order parameter across the transition is directly imprinted onto the propagators in the various color modes. In the SU(2) case, this leads, for instance, to a cusp in the electric and magnetic gluon susceptibilities as well as similar signatures in the ghost sector. We mention the possibility that such distinctive features of the transition could be measured in lattice simulations in the background field gauge studied here.Comment: 28 pages, 17 figures; published versio

Deconfinement transition in SU(N) theories from perturbation theory

We consider a simple massive extension of the Landau-DeWitt gauge for SU($N$) Yang-Mills theory. We compute the corresponding one-loop effective potential for a temporal background gluon field at finite temperature. At this order the background field is simply related to the Polyakov loop, the order parameter of the deconfinement transition. Our perturbative calculation correctly describes a quark confining phase at low temperature and a phase transition of second order for $N=2$ and weakly first order for $N=3$. Our estimates for the transition temperatures are in qualitative agreement with values from lattice simulations or from other continuum approaches. Finally, we discuss the effective gluon mass parameter in relation to the Gribov ambiguities of the Landau-DeWitt gauge.Comment: 10 pages, 3 figure

Yang-Mills correlators at finite temperature: A perturbative perspective

We consider the two-point correlators of Yang-Mills theories at finite temperature in the Landau gauge. We employ a model for the corresponding Yang-Mills correlators based on the inclusion of an effective mass term for gluons. The latter is expected to have its origin in the existence of Gribov copies. One-loop calculations at zero temperature have been shown to agree remarkably well with the corresponding lattice data. We extend on this and perform a one-loop calculation of the Matsubara gluon and ghost two-point correlators at finite temperature. We show that, as in the vacuum, an effective gluon mass accurately captures the dominant infrared physics for the magnetic gluon and ghost propagators. It also reproduces the gross qualitative features of the electric gluon propagator. In particular, we find a slight nonmonotonous behavior of the Debye mass as a function of temperature, however not as pronounced as in existing lattice results. A more quantitative description of the electric sector near the deconfinement phase transition certainly requires another physical ingredient sensitive to the order parameter of the transition.Comment: 16 pages, 12 figures ; Published version (PRD

Two-loop study of the deconfinement transition in Yang-Mills theories: SU(3) and beyond

We study the confinement-deconfinement phase transition of pure Yang-Mills theories at finite temperature using a simple massive extension of standard background field methods. We generalize our recent next-to-leading-order perturbative calculation of the Polyakov loop and of the related background field effective potential for the SU(2) theory to any compact and connex Lie group with a simple Lie algebra. We discuss in detail the SU(3) theory, where the two-loop corrections yield improved values for the first-order transition temperature as compared to the one-loop result. We also show that certain one-loop artifacts of thermodynamical observables disappear at two-loop order, as was already the case for the SU(2) theory. In particular, the entropy and the pressure are positive for all temperatures. Finally, we discuss the groups SU(4) and Sp(2) which shed interesting light, respectively, on the relation between the (de)confinement of static matter sources in the various representations of the gauge group and on the use of the background field itself as an order parameter for confinement. In both cases, we obtain first-order transitions, in agreement with lattice simulations and other continuum approaches.Comment: 35 pages, 20 figure