Local equilibrium of the quark-gluon plasma

Within kinetic theory, we look for local equilibrium configurations of the quark-gluon plasma by maximizing the local entropy. We use the well-established transport equations in the Vlasov limit, supplemented with the Waldmann-Snider collision terms. Two different classes of local equilibrium solutions are found. The first one corresponds to the configurations that comply with the so-called collisional invariants. The second one is given by the distribution functions that cancel the collision terms, representing the most probable binary interactions with soft gluon exchange in the t-channel. The two sets of solutions agree with each other if we go beyond these dominant processes and take into account subleading quark-antiquark annihilation/creation and gluon number non-conserving processes. The local equilibrium state appears to be colorful, as the color charges are not locally neutralized. Properties of such an equilibrium state are analyzed. In particular, the related hydrodynamic equations of a colorful fluid are derived. Possible neutralization processes are also briefly discussed.Comment: 20 pages; minor changes, to be published in Phys. Rev.

A remark on non-Abelian classical kinetic theory

It is known that non-Abelian classical kinetic theory reproduces the Hard Thermal/Dense Loop (HTL/HDL) effective action of QCD, obtained after integrating out the hardest momentum scales from the system, as well as the first higher dimensional operator beyond the HTL/HDL level. We discuss here its applicability at still higher orders, by comparing the exact classical effective action obtained in the static limit, with the 1-loop quantum effective potential. We remark that while correct types of operators arise, the classical colour algebra reproduces correctly the prefactor of the 4-point function $tr A_0^4$ only for matter in asymptotically high dimensional colour representations.Comment: 6 page

Gauge Invariance of Resummation Schemes: The QCD Partition Function

We pick up a method originally developed by Cheng and Tsai for vacuum perturbation theory which allows to test the consistency of different sets of Feynman rules on a purely diagrammatic level, making explicit loop calculations superfluous. We generalize it to perturbative calculations in thermal field theory and we show that it can be adapted to check the gauge invariance of physical quantities calculated in improved perturbation schemes. Specifically, we extend this diagrammatic technique to a simple resummation scheme in imaginary time perturbation theory. As an application, we check up to O(g^4) in general covariant gauge the gauge invariance of the result for the QCD partition function which was recently obtained in Feynman gauge.Comment: 29 pages, LaTeX, using RevTeX and feynmf.sty, Replacement: NO changes to the paper, TeX-source now additionally avaibl

Dynamics of Quark-Gluon-Plasma Instabilities in Discretized Hard-Loop Approximation

Non-Abelian plasma instabilities have been proposed as a possible explanation for fast isotropization of the quark-gluon plasma produced in relativistic heavy-ion collisions. We study the real-time evolution of these instabilities in non-Abelian plasmas with a momentum-space anisotropy using a hard-loop effective theory that is discretized in the velocities of hard particles. We extend our previous results on the evolution of the most unstable modes, which are constant in directions transverse to the direction of anisotropy, from gauge group SU(2) to SU(3). We also present first full 3+1-dimensional simulation results based on velocity-discretized hard loops. In contrast to the effectively 1+1-dimensional transversely constant modes we find subexponential behaviour at late times.Comment: 30 pages, 16 figures. v3 typos fixe

Classical transport equation in non-commutative QED at high temperature

We show that the high temperature behavior of non-commutative QED may be simply obtained from Boltzmann transport equations for classical particles. The transport equation for the charge neutral particle is shown to be characteristically different from that for the charged particle. These equations correctly generate, for arbitrary values of the non-commutative parameter theta, the leading, gauge independent hard thermal loops, arising from the fermion and the gauge sectors. We briefly discuss the generating functional of hard thermal amplitudes.Comment: 11 page

Transport equation for the photon Wigner operator in non-commutative QED

We derive an exact quantum equation of motion for the photon Wigner operator in non-commutative QED, which is gauge covariant. In the classical approximation, this reduces to a simple transport equation which describes the hard thermal effects in this theory. As an example of the effectiveness of this method we show that, to leading order, this equation generates in a direct way the Green amplitudes calculated perturbatively in quantum field theory at high temperature.Comment: 13 pages, twocolumn revtex4 styl

Non-perturbative thermal flows and resummations

We construct a functional renormalisation group for thermal fluctuations. Thermal resummations are naturally built in, and the infrared problem of thermal fluctuations is well under control. The viability of the approach is exemplified for thermal scalar field theories. In gauge theories the present setting allows for the construction of a gauge-invariant thermal renormalisation group.Comment: 16 pages, eq (38) added to match published versio

Production of gluons in the classical field model for heavy ion collisions

The initial stages of relativistic heavy ion collisions are studied numerically in the framework of a 2+1 dimensional classical Yang-Mills theory. We calculate the energy and number densities and momentum spectra of the produced gluons. The model is also applied to non central collisions. The numerical results are discussed in the light of RHIC measurements of energy and multiplicity and other theoretical calculations. Some problems of the present approach are pointed out.Comment: 9 pages, 11 figures, RevTeX; error in eq. (11) corrected, figures clarified, published in Phys. Rev.

Thermal fluctuations in the interacting pion gas

We derive the two-particle fluctuation correlator in a thermal gas of pi-mesons to the lowest order in an interaction due to a resonance exchange. A diagrammatic technique is used. We discuss how this result can be applied to event-by-event fluctuations in heavy-ion collisions, in particular, to search for the critical point of QCD. As a practical example, we determine the shape of the rapidity correlator.Comment: 12 pages, 4 figures, RevTe

A New Phase of Matter: Quark-Gluon Plasma Beyond the Hagedorn Critical Temperature

I retrace the developments from Hagedorn's concept of a limiting temperature for hadronic matter to the discovery and characterization of the quark-gluon plasma as a new state of matter. My recollections begin with the transformation more than 30 years ago of Hagedorn's original concept into its modern interpretation as the "critical" temperature separating the hadron gas and quark-gluon plasma phases of strongly interacting matter. This was followed by the realization that the QCD phase transformation could be studied experimentally in high-energy nuclear collisions. I describe here my personal effort to help develop the strangeness experimental signatures of quark and gluon deconfinement and recall how the experimental program proceeded soon to investigate this idea, at first at the SPS, then at RHIC, and finally at LHC. As it is often the case, the experiment finds more than theory predicts, and I highlight the discovery of the "perfectly" liquid quark-gluon plasma at RHIC. I conclude with an outline of future opportunities, especially the search for a critical point in the QCD phase diagram.Comment: To appear in {\em Melting Hadrons, Boiling Quarks} by Rolf Hagedorn and Johan Rafelski (editor), Springer Publishers, 2015 (open access