Heavy Quark Production at High Energy

We report on QCD radiative corrections to heavy quark production valid at high energy. The formulae presented will allow a matched calculation of the total cross section which is correct at O(\as^3) and includes resummation of all terms of order \as^3 [\as \ln (s/m^2)]^n. We also include asymptotic estimates of the effect of the high energy resummation. A complete description of the calculation of the heavy quark impact factor is included in an appendix.Comment: 32 pages (LaTeX) with three figures. Resubmission to agree with published version, which contains a new note added in proof and modifications of text of appendix

Scheme Dependence at Small x

We discuss the evolution of F_2^p at small x, emphasizing the uncertainties related to expansion, fitting, renormalization and factorization scheme dependence. We find that perturbative extrapolation from the measured region down to smaller x and lower Q^2 may become strongly scheme dependent.Comment: 8 pages, LaTeX with epsfig, 2 uuencoded figure

The Regularization of the Fermion Determinant in Chiral Quark Models

The momentum dependence of the quark self energy gives a physically motivated and consistent regularization of both the real and imaginary parts of the quark loop contribution to the meson action. We show that the amplitudes for anomalous processes are always reproduced correctly.Comment: 12/8 pages (b/l), plain TeX with harvmac, SphT93/13

The C-Theorem and Chiral Symmetry Breaking in Asymptotically Free Vectorlike Gauge Theories

We confront Cardy's suggested c-function for four-dimensional field theories with the spontaneous breaking of chiral symmetries in asymptotically free vectorlike gauge theories with fermions transforming according to different representations under the gauge group. Assuming that the infrared limit of the c-function is determined by the dimension of the associated Goldstone manifold, we find that this c-function always decreases between the ultraviolet and infrared fixed points.Comment: 8 pages, no figures, a few references adde

Incompatible sets of gradients and metastability

We give a mathematical analysis of a concept of metastability induced by incompatibility. The physical setting is a single parent phase, just about to undergo transformation to a product phase of lower energy density. Under certain conditions of incompatibility of the energy wells of this energy density, we show that the parent phase is metastable in a strong sense, namely it is a local minimizer of the free energy in an $L^1$ neighbourhood of its deformation. The reason behind this result is that, due to the incompatibility of the energy wells, a small nucleus of the product phase is necessarily accompanied by a stressed transition layer whose energetic cost exceeds the energy lowering capacity of the nucleus. We define and characterize incompatible sets of matrices, in terms of which the transition layer estimate at the heart of the proof of metastability is expressed. Finally we discuss connections with experiment and place this concept of metastability in the wider context of recent theoretical and experimental research on metastability and hysteresis.Comment: Archive for Rational Mechanics and Analysis, to appea

BFKL at NNLO

We present a recent determination of an approximate expression for the O(alpha_s^3) contribution chi_2 to the kernel of the BFKL equation. This includes all collinear and anticollinear singular contributions and is derived using duality relations between the GLAP and BFKL kernels.Comment: 8 pages. Talk presented at 12th International Conference on Elastic and Diffractive Scattering: Forward Physics and QCD, Hamburg, DESY, Germany, 21-25 May 200

Singularity theory study of overdetermination in models for L-H transitions

Two dynamical models that have been proposed to describe transitions between low and high confinement states (L-H transitions) in confined plasmas are analysed using singularity theory and stability theory. It is shown that the stationary-state bifurcation sets have qualitative properties identical to standard normal forms for the pitchfork and transcritical bifurcations. The analysis yields the codimension of the highest-order singularities, from which we find that the unperturbed systems are overdetermined bifurcation problems and derive appropriate universal unfoldings. Questions of mutual equivalence and the character of the state transitions are addressed.Comment: Latex (Revtex) source + 13 small postscript figures. Revised versio