Tom Steele

B.Sc. (University of Western Ontario) 1983
M.Sc. (University of Alberta) 1985
Ph.D. (University of Western Ontario) 1988

Quantum Chromodynamics (QCD) describes the strong force in terms of the fundamental interactions between quarks, elementary particles which provide the substructure of hadrons such as neutrons, protons and pions. QCD is one of the richest known gauge theories, exhibiting asymptotic freedom, and a non-trivial vacuum structure leading to spontaneous symmetry breaking. However, the property of asymptotic freedom implies that the QCD or strong coupling constant becomes large in the energy range of hadronic physics. Although this property is clearly desirable because of its relation to quark confinement, it implies that perturbative techniques, the standard tool for gauge field-theoretical calculations, have limited applicability in the nonperturbative regime of hadronic physics. Furthermore, the existence of a non-trivial QCD vacuum structure leads to effects that cannot be accommodated in a purely perturbative approach.

The dominant theme in my research is the development and application of theoretical techniques associated with the nonperturbative regime of QCD and hadronic physics. This research falls into several distinct categories:

• QCD sum-rule techniques provide a method for making theoretical predictions of the hadronic mass spectrum using analytical techniques (as opposed to computer simulations based on lattice techniques) which provide insight into the roles of non-perturbative effects. Research in this area include analysis of the scalar and pseudoscalar quark mesons and gluonium, novel applications of sum-rule techniques to hadronic contributions to anomalous magnetic moments, and development of fundamental inequalities which extend the ability of QCD sum-rules to make new phenomenological predictions.
• Gauge parameter dependence in QCD is a crucial constraint on the construction of observable quantities. Research in this area includes application of the Nielsen identities to study gauge dependence in on-shell renormalization schemes, and manifestly gauge invariant formulations of gauge theories.
• Pade approximations in QCD address the slowly-converging nature of the perturbative expansion in QCD either by predicting the next term in the perturbative expansion or by employing a Pade summation to estimate the aggregate effect of higher-order perturbative contributions. This research has included calculations used to verify the validity of the Pade techniques by comparison both with known higher-loop calculations and with perturbative contributions determined by renormalization-group techniques.