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

Bostonia Magazine. Volume 56

Founded in 1900, Bostonia magazine is Boston University's main alumni publication, which covers alumni and student life, as well as university activities, events, and programs

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

Algebra versus analysis in the theory of flexible polyhedra

Two basic theorems of the theory of flexible polyhedra were proven by completely different methods: R. Alexander used analysis, namely, the Stokes theorem, to prove that the total mean curvature remains constant during the flex, while I.Kh. Sabitov used algebra, namely, the theory of resultants, to prove that the oriented volume remains constant during the flex. We show that none of these methods can be used to prove the both theorems. As a by-product, we prove that the total mean curvature of any polyhedron in the Euclidean 3-space is not an algebraic function of its edge lengths.Comment: 5 pages, 5 figures; condition (iii) in Theorem 5 is correcte