Is Quantization of QCD Unique at the Non-Perturbative Level ?

We find that QCD in covariant gauge yields zero for the topological susceptibility, even at the nonperturbative level. The result is derived in two ways, one using translational invariance, and the other using the BRST Hamiltonian. Comparison with the canonical formalism suggests that QCD is not uniquely defined at the nonperturbative level. Supporting evidence is also provided in 1+1 dimensions. Our results imply that the strong CP problem admits a trivial resolution in covariant gauge, but obstacles remain for the U(1) problem.Comment: 5 pages, Previous version updated and an example in 1+1 dimensions supplie

A MASTER FORMULA FOR CHIRAL SYMMETRY BREAKING

We derive a master formula for chiral $SU(2)\times SU(2)$ breaking, based on the Veltman-Bell equations and the Peierls-Dyson relation. Our approach does not rely on the use of the soft pion limit or an expansion around the chiral limit, and yields exact results for on-shell pions. Threshold theorems for $\pi N\rightarrow \pi N$, $\gamma N\rightarrow \pi N$, $\pi N\rightarrow\pi\pi N$, $\gamma N\rightarrow \gamma\pi N$, $\gamma N\rightarrow \pi\pi N$ and $\pi N\rightarrow \pi\gamma N$ are recovered, and corrections to them are given. The reactions $\pi\rightarrow e\nu \gamma$, $\pi\rightarrow e\nu e^+e^-$, $\gamma\pi\rightarrow \gamma\pi$ and $\gamma\gamma\rightarrow \pi\pi$ are also discussed. A general formula for $\pi\pi$ scattering and a new one loop effective action are obtained. The new effective action reproduces the KSFR relation, and yields specific estimates for the pion polarisabilities. A detailed comparison with baryon-free chiral perturbation theory to one loop is made. An extension of our effective action to two loops is outlined.Comment: 119 pages + 7 Figures available from (I.Zahed

Electromagnetic Emission Rates and Spectral Sum Rules

The electromagnetic emission rates at SPS energies satisfy spectral constraints in leading order in the pion and nucleon densities. These constraints follow from the strictures of broken chiral symmetry. We saturate these constraints using available data, leading to model independent emission rates from a hadronic gas. With a simple fire-ball scenario, only large nucleon densities may account for the present CERES data.Comment: 4 pages (Latex), 2 embedded ps figures, espcrc1 style, talk given at Quark Matter 97, December 97, Tsukuba, Japa

Anterior and Posterior Corneal Astigmatism after Refractive Lenticule Extraction for Myopic Astigmatism

Purpose. To assess the amount and the axis orientation of anterior and posterior corneal astigmatism after refractive lenticule extraction (ReLEx) for myopic astigmatism. Methods. We retrospectively examined 53 eyes of 53 consecutive patients (mean age ± standard deviation, 33.2 ± 6.5 years) undergoing ReLEx to correct myopic astigmatism (manifest cylinder = 0.5 diopters (D)). Power vector analysis was performed with anterior and posterior corneal astigmatism measured with a rotating Scheimpflug system (Pentacam HR, Oculus) and refractive astigmatism preoperatively and 3 months postoperatively. Results. Anterior corneal astigmatism was significantly decreased, measuring 1.42 ± 0.73 diopters (D) preoperatively and 1.11 ± 0.53 D postoperatively (p<0.001, Wilcoxon signed-rank test). Posterior corneal astigmatism showed no significant change, falling from 0.44 ± 0.12 D preoperatively to 0.42 ± 0.13 D postoperatively (p=0.18). Refractive astigmatism decreased significantly, from 0.92 ± 0.51 D preoperatively to 0.27 ± 0.44 D postoperatively (p<0.001). The anterior surface showed with-the-rule astigmatism in 51 eyes (96%) preoperatively and 48 eyes (91%) postoperatively. By contrast, the posterior surface showed against-the-rule astigmatism in all eyes preoperatively and postoperatively. Conclusions. The surgical effects were largely attributed to the astigmatic correction of the anterior corneal surface. Posterior corneal astigmatism remained unchanged even after ReLEx for myopic astigmatism

Master Formula Approach to Chiral Symmetry Breaking: Pi-Pi scattering

The master formula approach to chiral symmetry breaking is used to analyze the phase shifts for $\pi\pi$ scattering in the elastic region. The results are in excellent agreement with the data for the phase shifts up to the K-K bar threshold. Our analysis shows that the pi-pi data near threshold in the scalar channel favors a large quark condensate in the vacuum, i.e. \sim -(240 MeV)^3.Comment: 17 pages, LaTeX, 1 postscript file of 12 figures in addition. Equation 2 is changed, the rest is the sam