We show that the general Lorentz-and CPT-violating extension of quantum electrodynamics is one-loop renormalizable. The one-loop Lorentz-violating beta functions are obtained, and the running of the coefficients for Lorentz and CPT violation is determined. Some implications for theory and experiment are discussed.

We demonstrate that the soft supersymmetry-breaking terms in a N = 1 theory can be linked by simple renormalisation group invariant relations which are valid to all orders of perturbation theory. In the special case of finite N = 1 theories, the soft terms preserve finiteness to all orders.

Four-point correlation functions of hypermultiplet bilinear composites are analysed in N = 2 superconformal field theory using the superconformal Ward identities and the analyticity properties of the composite operator superfields. It is shown that the complete amplitude is determined by a single arbitrary function of the two conformal cross-ratios of the space-time variables.

We explore the relationship between the DRED and NSVZ schemes. Using certain exact results for the soft scalar mass $\beta$-function, we derive the transformation of $\alpha^{\DRED}$ to $\alpha^{\NSVZ}$ through terms of order $\alpha^4$. We thus incidentally determine $\beta_{\alpha}^{\DRED}$ through four loops, and we compare our result to a previous Pad\'e Approximant prediction.Comment: 9 pages, including 1 figure. Plain TeX. Uses Harvmac and epsf. Version to be published in Phys. Lett. B. with minor corrections (and modified title

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