arXiv subjects
Publications and source records attributed to R. Delbourgo.
It is possible to determine a propapagator for heavy quarks to order 1/m in any covariant gauge, which applies universally to all quarks, by using the gauge technique. The leading behaviour is given by a _0F_2 function and the result is reliable in the infrared limit, accounting for soft-gluon corrections to the quark in internal loops.
The problem of how to obtain quasi-classical states for quantum groups is examined. A measure of quantum indeterminacy is proposed, which involves expectation values of some natural quantum group operators. It is shown that within any finite dimensional irreducible representation, the highest weight vector and those unitarily related to it are the quasi-classical states.
A knot-theoretic explanation is given for the rationality of the quenched QED beta function. At the link level, the Ward identity entails cancellation of subdivergences generated by one term of the skein relation, which in turn implies cancellation of knots generated by the other term. In consequence, each bare three-loop diagram has a rational Laurent expansion in the Landau gauge, as is verified by explicit computation. Comparable simplification is found to occur in scalar electrodynamics, when computed in the Duffin-Kemmer-Petiau formalism.
The subject of low energy photon-photon scattering is considered in arbitrary dimensional space-time and the interaction is widened to include scattering events involving an arbitrary number of photons. The effective interaction Lagrangian for these processes in QED has been determined in a manifestly invariant form. This generalisation resolves the structure of the weak-field Euler-Heisenberg Lagrangian and indicates that the component invariant functions have coefficients related, not only to the space-time dimension, but also to the coefficients of the Bernoulli polynomial.
We use a covariant supermultiplet theory to determine the primary coupling constant associated with several types of two-body meson decay. Despite the diverse range of decays considered the primary coupling constant is surprisingly uniform. We envisage the extension of the techniques to heavy quark cases, including as preliminary examples the calculation of the $D^{*+}$ and $D^{*0}$ total decay widths with results $57.7 \pm 1.5$ KeV and $42.5 \pm 2.6$ KeV respectively, as well as some predictions about $D^*$ and $B^*$ radiative decays. (3 uuencoded Postscript Files are appended at the end of the TexFile.)
One of the interesting features about field theories in odd dimensions is the induction of parity violating terms and well-defined {\em finite} topological actions via quantum loops if a fermion mass term is originally present and conversely. Aspects of this issue are illustrated for electrodynamics in 2+1 and 4+1 dimensions. (3 uuencoded Postscript Files are appended at the end of the TexFile.)
We analyse the Lorentz structures of weak decay matrix elements bewteen meson states of arbitrary spin. Simplifications arise in the transition amplitudes for a heavy meson decaying into a light one via a Bethe-Salpeter approach which incorporates heavy quark symmetry. Phenomenological consequences on several semileptonic, nonleptonic and FCNC induced decays of heavy flavoured mesons are derived and discussed.
Lorentz covariant wave functions for meson and baryon supermultiplets are simply derived by boosting $SU(2)_J$ representations corresponding to multiquark systems at rest.