James S. Ball

Dual QCD: A review

Abstract We review the attempts to use dual (electric) vector potentials rather than the standard magnetic vector potentials to describe QCD, particularly in the infrared regime. The use of dual potentials is motivated by the fact that in classical electrodynamics, in a medium with a dielectric constant vanishing at small momenta (as is believed to be the case in QCD), electric potentials provide a far more convenient language than do magnetic potentials. To begin with, we outline attempts to construct the QCD Lagrangian in terms of dual potentials and describe the various possibilities, their shortcomings and advantages, which so far exist. We then proceed to use the most attractive (albeit consistent as a field theory only at the tree leve l) of these Lagrangians in a number of applications. We show that it describes a non-Abelian dual superconductor (so that it automatically confines color), derive the static quark-antiquark potential, and various temperature dependent effects, such as deconfinement and chiral symmetry breaking.

Wave Equations and Inverse Solutions for Soft Tissue

Ultrasound has been used in the echo mode as a diagnostic tool for many years. The images produced by the echo mode are not qualitative and do not measure absolute tissue properties. Rather, echo-mode images display the changes in acoustic impedance. Thus, the boundaries of tissues are imaged. Such images are of value for study of anatomy and tissue morphology. Tumors are detected by their shape and not by their tissue type. Thus, classification of malignant or benign tumors is difficult by use of echo-mode imaging alone. The recently developed straight-line ultrasound transmission tomographic methods provide images which are qualitative and absolute (not relative), but have inferior resolution compared to the echo methods [Greenleaf, et al., 1978].

The quark propagator in axial gauge

Abstract We study the Dyson equation for the quark propagator S ( p ) in QCD, making use of both the Ward identity and an infrared singular gluon propagator naively corresponding to a linear confining potential. We find that, assuming massless free quarks, the singularity at p 2 = 0 in S ( p ) is greatly softened by the gluon infrared singularity, perhaps hinting at confinement. We also find that chiral symmetry may be, but does not have to be, broken.

Infrared properties of the glue propagator in non-abelian gauge theories

Abstract In a pure Yang-Mills theory, the Dyson equation for the gluon propagator is studied in the infrared regime, under the assumption that, as in QED, only those parts of the proper gluon vertex functions determined by the Ward identities are relevant. The calculations are all carried out in the axial gauge. With a number of simplifying assumptions the resulting integral equation for the gluon propagator can be solved in the IR regime. The solution displays a power singularity in the IR for the renormalized coupling constant g ( q 2 ).

Phenomenological implications of colliding Regge poles and cuts

It is suggested that Regge pole-cut combinations should, in the t < 0 region and until high energies are reached, always be parametrized simply by a complex conjugate pair of Regge poles, with no explicit contribution from the Regge cut. Effects of Regge cuts, at moderate energies, are well represented by complex pairs of poles. Some consequences of this suggestion are described.

An effective action describing long-range Yang-Mills theory

Abstract Using previously derived expressions for axial gauge propagators and vertex functions in the infrared limit of pure Yang-Mills theory, we show that at long-range quantum Yang-Mills theory is equivalent to a classical Yang-Mills theory in an anisotropic and inhomogeneous medium, the QCD vacuum. The properties of this classical theory are described and possible applications are outlined.

Half-Range Generalized Hermite Polynomials and the Related Gaussian Quadratures

A method is developed for calculating the recurrence coefficients for half-range generalized Hermite polynomials. These are orthogonal polynomials with measure

An analytic calculation of the weak field limit of the static color dielectric constant

x^{\gamma}e^{-x^{2}}

Automatic Computation of Zeros of Bessel Functions and Other Special Functions

on the interval (

Orthogonal polynomials, Gaussian quadratures, and PDEs

0,\infty