Gauge Fixing and Observables in General Relativity

The conventional group of four-dimensional diffeomorphisms is not realizeable as a canonical transformation group in phase space. Yet there is a larger field-dependent symmetry transformation group which does faithfully reproduce 4-D diffeomorphism symmetries. Some properties of this group were first explored by Bergmann and Komar. More recently the group has been analyzed from the perspective of projectability under the Legendre map. Time translation is not a realizeable symmetry, and is therefore distinct from diffeomorphism-induced symmetries. This issue is explored further in this paper. It is shown that time is not "frozen". Indeed, time-like diffeomorphism invariants must be time-dependent. Intrinsic coordinates of the type proposed by Bergmann and Komar are used to construct invariants. Lapse and shift variables are retained as canonical variables in this approach, and therefore will be subject to quantum fluctuations in an eventual quantum theory. Concepts and constructions are illustrated using the relativistic classical and quantum free particle. In this example concrete time-dependent invariants are displayed and fluctuation in proper time is manifest.Comment: Contribution to the Proceedings of Spacetime and Fundamental Interactions: Quantum Aspects, May, 2003, honoring the 65'th birthday of A. P. Balachandra

Probing the Phase Boundary between Hadronic Matter and the Quark-Gluon-Plasma in Relativistic Heavy Ion Collisions

We discuss recent data on particle production with emphasis on the degree of thermal and chemical equilibration achieved. The data are interpreted in terms of a resonance gas model. The phase boundary constructed between the resonance gas and the quark-gluon plasma is shown to be very close to the deduced parameters characterizing the hadronic fireball at freeze-out.Comment: 7 pages, latex, 6 figures, 1 table submitted to Nuclear Physics A, dedicated to Gerry Brown in honor of his 70th birthda

On Charm Production near the Phase Boundary

We discuss aspects of the statistical hadronization model for the production of mesons with open and hidden charm in ultra-relativistic nuclear collisions. Emphasis is placed on what can be inferred from the dependence of the yield of charmonia on the number of participants in the collisions.Comment: Invited Paper, NAN Conference, Darmstadt, Oct. 2000, final version, expanded discussion on results at collider energies, Nucl. Phys. A. (in print). Dedicated to Achim Richter in honor of his 60th birthda

Particle Production in Heavy Ion Collisions

The status of thermal model descriptions of particle production in heavy ion collisions is presented. We discuss the formulation of statistical models with different implementation of the conservation laws and indicate their applicability in heavy ion and elementary particle collisions. We analyze experimental data on hadronic abundances obtained in ultrarelativistic heavy ion collisions, in a very broad energy range starting from RHIC/BNL ($\sqrt s=200$ A GeV), SPS/CERN ($\sqrt s\simeq 20$ A GeV) up to AGS/BNL ($\sqrt s\simeq 5$ A GeV) and SIS/GSI ($\sqrt s\simeq 2$ A GeV) to test equilibration of the fireball created in the collision. We argue that the statistical approach provides a very satisfactory description of experimental data covering this wide energy range. Any deviations of the model predictions from the data are indicated. We discuss the unified description of particle chemical freeze--out and the excitation functions of different particle species. At SPS and RHIC energy the relation of freeze--out parameters with the QCD phase boundary is analyzed. Furthermore, the application of the extended statistical model to quantitative understanding of open and hidden charm hadron yields is considered.Comment: Invited review for Quark Gluon Plasma 3, eds. R. C. Hwa and Xin-Nian Wang, World Scientific Publishin

The horn, the hadron mass spectrum and the QCD phase diagram - the statistical model of hadron production in central nucleus-nucleus collisions

We present the status of the description of hadron production in central nucleus-nucleus collisions within the statistical model . The recent inclusion of very high-mass resonances and the sigma meson leads to an improved description of the data, in particular the energy dependence of the K+/pi+ ratio at SPS energies (``the horn''). The connection to the QCD phase diagram is discussed.Comment: 4 pages, 3 figures; presented at the Nucleus-Nucleus 2009 conference, Beijing, Aug. 200

The thermal model on the verge of the ultimate test: particle production in Pb-Pb collisions at the LHC

We investigate the production of hadrons in nuclear collisions within the framework of the thermal (or statistical hadronization) model. We discuss both the ligh-quark hadrons as well as charmonium and provide predictions for the LHC energy. Even as its exact magnitude is dependent on the charm production cross section, not yet measured in Pb-Pb collisions, we can confidently predict that at the LHC the nuclear modification factor of charmonium as a function of centrality is larger than that observed at RHIC and compare the experimental results to these predictions.Comment: 4 pages, 3 figures; proceedings of QM201

The statistical model in Pb-Pb collisions at the LHC

We briefly review the predictions of the thermal model for hadron production in comparison to latest data from RHIC and extrapolate the calculations to LHC energy. Our main emphasis is to confront the model predictions with the recently released data from ALICE at the LHC. This comparison reveals an apparent anomaly for protons and anti-protons which we discuss briefly. We also demonstrate that our statistical hadronization predictions for J/$\psi$ production agree very well with the most recent LHC data, lending support to the picture in which there is complete charmonium melting in the quark-gluon plasma (QGP) followed by statistical generation of J/$\psi$ mesons at the phase boundary.Comment: 4 pages, 3 figures, proceedings of QM201