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

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