Momentum subtraction and the R-ratio

We determine the R-ratio for massless quarks in several renormalization schemes to various loop orders. These are the momentum subtraction schemes of Celmaster and Gonsalves as well as the minimal momentum subtraction scheme. The dependence of the R-ratio on the schemes is analysed.Comment: 27 latex pages, 36 figures, anc directory contains txt file with electronic version of main equation

Algorithm for Computing the \BETA-Function of Quantum Electrodynamics in the Large N_f Expansion

By considering corrections to the asymptotic scaling functions of the photon and electron in quantum electrodynamics with \Nf flavours, we solve the skeleton Dyson equations at O(1/\Nf) in the large \Nf expansion at the $d$-dimensional critical point of the theory and deduce the critical exponent $\beta^\prime(g_c)$, in arbitrary dimensions, and subsequently present a method for computing higher order corrections to $\beta(g)$.Comment: latex file, 22 pages, 12 figures available on request from the author, LTH-29

Gauged Nambu-Jona-Lasinio Model at O(1/N) with and without a Chern-Simons Term

We solve the gauged Nambu--Jona-Lasinio model at leading order in the large $N$ expansion by computing the anomalous dimensions of all the fields of the model and other gauge independent critical exponents by examining the scaling behaviour of the Schwinger Dyson equation. We then restrict to the three dimensional model and include a Chern Simons term to discover the $\theta$-dependence of the same exponents where $\theta$ is the Chern Simons coupling.Comment: 10 pages (latex), 2 figures (available from author on request), LTH-31

Computation of Critical Exponent \eta at O(1/N^3) in the Four Fermi Model in Arbitrary Dimensions

We solve the conformal bootstrap equations of the four fermi model or $O(N)$ Gross Neveu model to deduce the fermion anomalous dimension of the theory at $O(1/N^3)$ in arbitrary dimensions.Comment: 21 pages, latex, 6 figures (available from the author on request), LTH-31