2-Group Representations for Spin Foams

Just as 3d state sum models, including 3d quantum gravity, can be built using categories of group representations, "2-categories of 2-group representations" may provide interesting state sum models for 4d quantum topology, if not quantum gravity. Here we focus on the "Euclidean 2-group", built from the rotation group SO(4) and its action on the group of translations of 4d Euclidean space. We explain its infinite-dimensional unitary representations, and construct a model based on the resulting representation 2-category. This model, with clear geometric content and explicit "metric data" on triangulation edges, shows up naturally in an attempt to write the amplitudes of ordinary quantum field theory in a background independent way.Comment: 8 pages; to appear in proceedings of the XXV Max Born Symposium: "The Planck Scale", Wroclaw, Polan

Quantum Potential Approach to Class of Cosmological Models

In this paper we discuss the quantum potential approach of Bohm in the context of quantum cosmological model. This approach makes it possible to convert the wavefunction of the universe to a set of equations describing the time evolution of the universe. Following Ashtekar et.\ al., we make use of quantum canonical transformation to cast a class of quantum cosmological models to a simple form in which they can be solved explicitly, and then we use the solutions do recover the time evolution.Comment: The corrected version of gr-qc/9506081, 18 pages LaTeX, to appear in Classical and Quantum Gravit

Doubly Special Relativity and de Sitter space

In this paper we recall the construction of Doubly Special Relativity (DSR) as a theory with energy-momentum space being the four dimensional de Sitter space. Then the bases of the DSR theory can be understood as different coordinate systems on this space. We investigate the emerging geometrical picture of Doubly Special Relativity by presenting the basis independent features of DSR that include the non-commutative structure of space-time and the phase space algebra. Next we investigate the relation between our geometric formulation and the one based on quantum $\kappa$-deformations of the Poincar\'e algebra. Finally we re-derive the five-dimensional differential calculus using the geometric method, and use it to write down the deformed Klein-Gordon equation and to analyze its plane wave solutions.Comment: 26 pages, one formula (67) corrected; some remarks adde

Report from NA49

The most recent data of NA49 on hadron production in nuclear collisions at CERN SPS energies are presented. Anomalies in the energy dependence of pion and kaon production in central Pb+Pb collisions are observed. They suggest that the onset of deconfinement is located at about 30 AGeV. Large multiplicity and transverse momentum fluctuations are measured for collisions of intermediate mass systems at 158 AGeV. The need for a new experimental programme at the CERN SPS is underlined.Comment: invited talk presented at Quark Matter 2004, 10 page

System-size dependence of strangeness production in nucleus-nucleus collisions at sqrt{s_{NN}}=17.3 GeV

Emission of pi, K, phi and Lambda was measured in near-central C+C and Si+Si collisions at 158 AGeV beam energy. Together with earlier data for p+p, S+S and Pb+Pb, the system-size dependence of relative strangeness production in nucleus-nucleus collisions is obtained. Its fast rise and the saturation observed at about 60 participating nucleons can be understood as onset of the formation of coherent partonic subsystems of increasing size.Comment: Phys.Rev.Lett in print; version2: changes made according to the request of the referee

Rapidity and transverse momentum dependence of pion-pion Bose-Einstein correlations measured at 20, 30, 40, 80, and 158 AGeV beam energy

Preliminary results on pion-pion Bose-Einstein correlations in central Pb+Pb collisions measured by the NA49 experiment are presented. Rapidity as well as transverse momentum dependence of the HBT-radii are shown for collisions at 20, 30, 40, 80, and 158 AGeV beam energy. Including results from AGS and RHIC experiments only a weak energy dependence of the radii is observed. Based on hydrodynamical models parameters like lifetime and geometrical radius of the source are derived from the dependence of the radii on transverse momentum.Comment: 5 pages, 4 figures, contribution to the Quark Matter conference, Oakland, USA, Jan 11-17, 200

Multistrange Hyperon Production in Pb+Pb collisions at 30, 40, 80 and 158 A⋅\cdotGeV

A non-monotonic energy dependence of the $K^{+} / \pi^{+}$ ratio with a sharp maximum close to 30 A$\cdot$GeV is observed in central Pb+Pb collisions. Within a statistical model of the early stage, this is interpreted as a sign of the phase transition to a QGP, which causes a sharp change in the energy dependence of the strangeness to entropy ratio. This observation naturally motivates us to study the production of multistrange hyperons ($\Xi$, $\Omega$) as a function of the beam energy. Furthermore it was suggested that the kinematic freeze-out of $\Omega$ takes place directly at QGP hadronization. If this is indeed the case, the transverse momentum spectra of the $\Omega$ directly reflect the transverse expansion velocity of a hadronizing QGP. In this report we show preliminary NA49 results on $\Omega^{-}$ and $\bar{\Omega}^{+}$ production in central Pb+Pb collisions at 40 and 158 A$\cdot$GeV and compare them to measurements of $\Xi^{-}$ and $\bar{\Xi}^{+}$ production in central Pb+Pb collisions at 30, 40, 80 and 158 A$\cdot$GeV.Comment: Presented at 25th International School of Nuclear Physics, Erice, Italy, to be published in Progress in Particle and Nuclear Physics, 3 pages, 4 figure

Deuteron production in central Pb + Pb collisions at 158-A-GeV

Experimental results on deuteron emission from central Pb+Pb collisions (E_beam=158A GeV, fixed target), obtained by NA49 at the CERN SPS accelerator, are presented. The transverse mass m_t distribution was measured near mid-rapidity (2.0<y<2.5) in the range of 0<m_t-m_0<0.9 GeV/c2 (0<p_t<2.0 GeV/c) for the 4% most central collisions. An exponential fit gives an inverse slope T_d=(450ą30) MeV and a yield dN_d/dy=0.34ą0.03. The coalescence factor B2(m_t=m_0)=(3.5ą1.0)ˇ10^4 GeV^2 and its m_t-dependence are determined and discussed in terms of a model that includes the collective expansion of the source created in a collision. The derived Gaussian size parameter R_G of the emission volume is consistent with earlier HBT results on the source of pion emission

The NA49 large acceptance hadron detector

The NA49 detector is a wide acceptance spectrometer for the study of hadron production in p+p, p+A, and A+A collisions at the CERN SPS. The main components are 4 large volume TPCs for tracking and particle identification via $dE/dx$. TOF scintillator arrays complement particle identification. Calorimeters for transverse energy determination and triggering, a detector for centrality selection in p+A collisions, and beam definition detectors complete the set-up. A description of all detector components is given with emphasis on new technical realizations. Performance and operational experience are discussed in particular with respect to the high track density environment of central Pb+Pb collisions