Domain Wall Fermions with Exact Chiral Symmetry

We show how the standard domain wall action can be simply modified to allow arbitrarily exact chiral symmetry at finite fifth dimensional extent. We note that the method can be used for both quenched and dynamical calculations. We test the method using smooth and thermalized gauge field configurations. We also make comparisons of the performance (cost) of the domain wall operator for spectroscopy compared to other methods such as the overlap-Dirac operator and find both methods are comparable in cost.Comment: revtex, 37 pages, 11 color postscript figure

Universal Scaling of the Chiral Condensate in Finite-Volume Gauge Theories

We confront exact analytical predictions for the finite-volume scaling of the chiral condensate with data from quenched lattice gauge theory simulations. Using staggered fermions in both the fundamental and adjoint representations, and gauge groups SU(2) and SU(3), we are able to test simultaneously all of the three chiral universality classes. With overlap fermions we also test the predictions for gauge field sectors of non-zero topological charge. Excellent agreement is found in most cases, and the deviations are understood in the others.Comment: Expanded discussion of overlap fermion results. 17 pages revtex, 7 postscript figure

Finite-Volume Scaling of the Quenched Chiral Condensate

In the large-volume limit $V\to\infty$ with $V << 1/m_{\pi}^4$ the mass-dependent chiral condensate is predicted to satisfy exact finite-volume scaling laws that fall into three major universality classes. We test these analytical predictions with staggered fermions and overlap fermions in gauge field sectors of fixed topological charge $\nu$.Comment: Talk at Lattice99(topology), 3 page

The impact of Chinese import penetration on the South African manufacturing sector

This article uses a Chenery-type decomposition and econometric estimation to evaluate the impact of Chinese trade on production and employment in South African manufacturing from 1992 to 2010. The results suggest that increased import penetration from China caused South African manufacturing output to be 5 per cent lower in 2010 than it otherwise would have been. The estimated reduction of total employment in manufacturing as a result of trade with China is larger – in 2010 about 8 per cent – because the declines in output were concentrated on labour-intensive industries and because the increase in imports raised labour productivity within industries

An alternative to domain wall fermions

We define a sparse hermitian lattice Dirac matrix, $H$, coupling $2n+1$ Dirac fermions. When $2n$ fermions are integrated out the induced action for the last fermion is a rational approximation to the hermitian overlap Dirac operator. We provide rigorous bounds on the condition number of $H$ and compare them to bounds for the higher dimensional Dirac operator of domain wall fermions. Our main conclusion is that overlap fermions should be taken seriously as a practical alternative to domain wall fermions in the context of numerical QCD.Comment: Revtex Latex, 26 pages, 1 figure, a few minor change

Generalised Spin Projection for Fermion Actions

The majority of compute time doing lattice QCD is spent inverting the fermion matrix. The time that this takes increases with the condition number of the matrix. The FLIC(Fat Link Irrelevant Clover) action displays, among other properties, an improved condition number compared to standard actions and hence is of interest due to potential compute time savings. However, due to its two different link sets there is a factor of two cost in floating point multiplications compared to the Wilson action. An additional factor of two has been attributed due to the loss of the so-called spin projection trick. We show that any split-link action may be written in terms of spin projectors, reducing the additional cost to at most a factor of two. Also, we review an efficient means of evaluating the clover term, which is additional expense not present in the Wilson action.Comment: 4 page

Comment on Path Integral Derivation of Schr\"odinger Equation in Spaces with Curvature and Torsion

We present a derivation of the Schr\"odinger equation for a path integral of a point particle in a space with curvature and torsion which is considerably shorter and more elegant than what is commonly found in the literature.Comment: LaTeX file in sr

Parsec Scale Properties of Markarian 501

We present the results of a high angular resolution study of the BL Lac object Markarian 501 in the radio band. We consider data taken at 14 different epochs, ranging between 1.6 GHz and 22 GHz in frequency, and including new Space VLBI observations obtained on 2001 March 5 and 6 at 1.6 and 5 GHz. We study the kinematics of the parsec-scale jet and estimate its bulk velocity and orientation with respect to the line of sight. Limb brightened structure in the jet is clearly visible in our data and we discuss its possible origin in terms of velocity gradients in the jet. Quasi-simultaneous multi-wavelength observations allow us to map the spectral index distribution and to compare it to the jet morphology. Finally, we estimate the physical parameters of the parsec-scale jet.Comment: accepted for publication in ApJ; 24 pages with 17 figures (fig. 1 and fig. 2 available only as .jpg files

Interacting Bose and Fermi gases in low dimensions and the Riemann hypothesis

We apply the S-matrix based finite temperature formalism to non-relativistic Bose and Fermi gases in 1+1 and 2+1 dimensions. In the 2+1 dimensional case, the free energy is given in terms of Roger's dilogarithm in a way analagous to the relativistic 1+1 dimensional case. The 1d fermionic case with a quasi-periodic 2-body potential provides a physical framework for understanding the Riemann hypothesis.Comment: version 3: additional appendix explains how the $\nu$ to $1-\nu$ duality of Riemann's $\zeta (\nu)$ follows from a special modular transformation in a massless relativistic theor