Geometric and Renormalized Entropy in Conformal Field Theory

In statistical physics, useful notions of entropy are defined with respect to some coarse graining procedure over a microscopic model. Here we consider some special problems that arise when the microscopic model is taken to be relativistic quantum field theory. These problems are associated with the existence of an infinite number of degrees of freedom per unit volume. Because of these the microscopic entropy can, and typically does, diverge for sharply localized states. However the difference in the entropy between two such states is better behaved, and for most purposes it is the useful quantity to consider. In particular, a renormalized entropy can be defined as the entropy relative to the ground state. We make these remarks quantitative and precise in a simple model situation: the states of a conformal quantum field theory excited by a moving mirror. From this work, we attempt to draw some lessons concerning the ``information problem'' in black hole physicsComment: 35 pages, 4 figures available on request to [email protected], use Phyzzx, PUPT-1454, IASSNS-HEP 93/8

Delta G from high pT events at SMC and high pT analysis at COMPASS

Measurements of the longitudinal spin cross section asymmetry for deep inelastic muon-nucleon interactions with two high transverse momentum hadrons ($p_T >$ 0.7 GeV) in the final state are presented for SMC data for polarized proton and deuteron and for data on polarized deuteron from COMPASS taken in 2002 and 2003. The muon asymmetries determined with a cut on $Q^2>$ 1 GeV$^2$ in SMC are: $A_p = 0.03 \pm 0.057\pm 0.01$ and $A_d = 0.070 \pm 0.076 \pm 0.010$, respectively. From these values a gluon polarization $\Delta G /G = -0.20\pm 0.28\pm 0.10$ was obtained at an average fraction of nucleon momentum carried by gluons $\eta = 0.07$. The measured asymmetry (with cut on $Q^2>$ 1 GeV$^2$) in COMPASS is $(A_d/D) = -0.015 \pm 0.08 \pm 0.013$ where D is depolarization factor and the gluon polarization $\Delta G /G = 0.06\pm 0.31\pmComment: 4 pages, 3 figures, Talk given at 10-th International Conference Baryons04, October 25-29, 2004, Ecole Polytechnique, Palaiseau, Franc

Dynamical Moving Mirrors and Black Holes

A simple quantum mechanical model of $N$ free scalar fields interacting with a dynamical moving mirror is formulated and shown to be equivalent to two-dimensional dilaton gravity. We derive the semi-classical dynamics of this system, by including the back reaction due to the quantum radiation. We develop a hamiltonian formalism that describes the time evolution as seen by an asymptotic observer, and write a scattering equation that relates the in-falling and out-going modes at low energies. At higher incoming energy flux, however, the classical matter-mirror dynamics becomes unstable and the mirror runs off to infinity. This instability provides a useful paradigm for black hole formation and introduces an analogous information paradox. Finally, we propose a new possible mechanism for restoring the stability in the super-critical situation, while preserving quantum coherence. This mechanism is based on the notion of an effective time evolution, that takes into account the quantum mechanical effect of the measurement of the Hawking radiation on the state of the infalling matter.Comment: 37 pages, 5 figures attached, epsf, harvmac, PUPT-143

Gamma^*, Z^* production in polarised p-p scattering as a probe of the proton spin structure

We present the results of a detailed study of the large transverse momentum Drell-Yan process, pp --> (Gamma^*, Z^*)X --> l^+l^- X at collider energies, with either one or both protons polarised, allowing the study of single- and double-spin asymmetries respectively. We show how these asymmetries obtained from angular distributions of the leptons in the Gamma^* (or Z^*) rest-frame, can be used to get information on the polarised parton distributions. Numerical results for the asymmetries and the cross-sections are presented, and the sensitivity of the asymmetries to the initial parton distributions indicates that these can be used as effective probes of the spin structure of the proton.Comment: Latex, 9 pages, 4 figures available on request, CERN-TH.6997/9

Frequency permutation arrays

Motivated by recent interest in permutation arrays, we introduce and investigate the more general concept of frequency permutation arrays (FPAs). An FPA of length n=m lambda and distance d is a set T of multipermutations on a multiset of m symbols, each repeated with frequency lambda, such that the Hamming distance between any distinct x,y in T is at least d. Such arrays have potential applications in powerline communication. In this paper, we establish basic properties of FPAs, and provide direct constructions for FPAs using a range of combinatorial objects, including polynomials over finite fields, combinatorial designs, and codes. We also provide recursive constructions, and give bounds for the maximum size of such arrays.Comment: To appear in Journal of Combinatorial Design

Open Budgets. Transform Lives. The Open Budget Survey 2008

Provides a comparative measure of government budget transparency in eighty-five countries. Discusses contributing factors and makes recommendations for improving transparency, increasing public participation, and strengthening accountability oversight

Polarized parton distributions in perturbative QCD

We review the main results of next-to-leading order QCD analyses of polarized deep-inelastic scattering data, with special attention to the assessment of theoretical uncertainties.Comment: 4 pages Latex, 1 ps figure. Talk given at NUCLEON '99, Frascati(Italy), June 7-9 199

The challenge of water provision in rural Tanzania

Despite significant recent investment, levels of access to clean drinking water in Tanzania remain similar to those of 20 years ago. Why is it that although money has been flowing, water continues to trickle

Normal Ordering for Deformed Boson Operators and Operator-valued Deformed Stirling Numbers

The normal ordering formulae for powers of the boson number operator $\hat{n}$ are extended to deformed bosons. It is found that for the `M-type' deformed bosons, which satisfy $a a^{\dagger} - q a^{\dagger} a = 1$, the extension involves a set of deformed Stirling numbers which replace the Stirling numbers occurring in the conventional case. On the other hand, the deformed Stirling numbers which have to be introduced in the case of the `P-type' deformed bosons, which satisfy $a a^{\dagger} - q a^{\dagger} a = q^{-\hat{n}}$, are found to depend on the operator $\hat{n}$. This distinction between the two types of deformed bosons is in harmony with earlier observations made in the context of a study of the extended Campbell-Baker-Hausdorff formula.Comment: 14 pages, Latex fil

The strength of small-instanton amplitudes in gauge theories with compact extra dimensions

We study instanton effects in theories with compact extra dimensions. We perform an instanton calculation in a 5d theory on a circle of radius R, with gauge, scalar, and fermion fields in the bulk of the extra dimension. We show that, depending on the matter content, instantons of size rho << R can dominate the amplitude. Using deconstruction as an ultraviolet definition of the theory allows us to show, in a controlled approximation, that for a small number of bulk fermions, the amplitude for small size instantons exponentially grows as e^{O(1)R/rho}.Comment: Title modified, references added, typos corrected. Version to appear in JHEP. 24 pages, 1 figur