In Memoriam Professor George Leibbrandt of the University of Guelph 1937 - 2001

George began his career in Theoretical Physics at McMaster University, obtaining a B.Sc. there in 1961. He then went on to carry out graduate work at McGill University, getting an M.Sc. and then a Ph.D. there, completing his studies in 1967. Shortly before the defense of his thesis, he took up a position in the Department of Mathematics and Statistics at the University of Guelph in 1966, a position he retained until his death in 2001.

  George enjoyed a long, productive and stimulating career in theoretical physics. He actively participated in the life of both the mathematics and physics departments at the University of Guelph, and was a well-known and much admired figure in each. Throughout his career, he supervised 10 postdoctoral fellows and 8 graduate students. He enjoyed the collegiality of his fellow researchers in theoretical physics throughout Southern Ontario, and participated regularly in the activities of the Guelph-Waterloo Physics Institute and in special events held at Toronto, Western, and McMaster.

His expertise in theoretical physics took him to some of the most prestigious institutions around the world, including Imperial College, Cambridge University, CERN, Harvard, and the ICTP in Trieste. He won two Humboldt Fellowships and was twice a Bye Fellow at Cambridge.

George's expertise was in gauge field theories. He was one of the first people to apply dimensional regularization to perturbative loop corrections in quantum gravity. The technique -- which involves calculating divergent integrals by analytically continuing in the number of spacetime dimensions -- was still quite new at the time, and George became one of the first experts on its application to quantum field theory.

In the 1980s George moved on to study field theories in non-covariant gauges. All standard model interactions respect the principle of gauge invariance, which allows for a redefinition of the 4-vector potential associate with a force according to a certain prescription. The simplest example is the modification of the vector potential in electromagnetism by the addition of the gradient of an arbitrary function; if you add such a gradient to the vector potential, both the electric and magnetic fields remain unchanged. In order to calculate in a quantum gauge field theory, it is necessary to "fix the gauge" ie choose a particular form of constraint on the gauge field (eg the photon or gluon) which eliminates the redundant gradient terms. In the 1970s this was almost always done covariantly, ie. in a manner that manifestly respected Lorentz invariance. However, while physical observations cannot depend on this choice of constraint, little was known about how to carry out calculations when the constaint was chosen non-covariantly.

George was one of the pioneers in demonstrating how to carry out quantum field theoretic corrections for this case, in a context which came to be referred to as a "non-covariant gauge" choice. His prescription for treating these cases came to be known as the "Mandlestam-Leibbrandt" prescription, named after both George and Stanly Mandlestam, who also worked on this subject. The techniques they developed became essential in demonstrating the finiteness of certain field theories such as N=4 Supersymmetric Yang-Mills theories.

In 1999 George was asked to become a founding member of the Perimeter Institute for Theoretical Physics, a task to which he dedicated himself wholeheartedly. He worked closely with the principal donor, Mike Lazaridis, and with Howard Burton, its executive director. George was very concerned that the Institute fulfil its mandate to be a premier place for research in theoretical physics, and he spent many volunteer hours attending board meetings, going through architectural plans, and participating in discussions concerning its scientific merit.

George will always be remembered for his kindness and patience. Always ready to help out a student or colleague in need, he had a way of providing encouragement just when you needed it most. His modesty concerning his own accomplishments in physics did not do justice to their importance. He will be sorely missed.

Dr. Robert Mann, University of Waterloo

George Leibbrandt 1937 - 2001

Noncovariant gauges in particle physics, renormalization in Yang-Mills theory, quantum gravity, and Chern-Simons theory.

The main research activities are in quantum field theory, specifically in the unification and mathematical treatment of gauge theories. It seems that all viable field theories are gauge theories. For instance, the theory of gravity is a gauge theory and so is the theory describing the strong interactions. The theory of superstrings which endeavours to combine Einstein's general relativity with quantum mechanics, is the most radical gauge theory.

Some of the most recent gauge theories are not only mathematically complicated but also conceptually difficult to follow. In order to extract useful information from these theories, researchers need to use clever techniques which reduce the horrendous algebra and thus make the inherent properties transparent. One such approach is to replace covariant gauges like the Feynman gauge by physical (or noncovariant) gauges such as the light-cone gauge, or the Coulomb gauge. Since 1983 physical gauges have become increasingly popular, especially in such sophisticated theories as quantum chromodynamics and superstrings.

Current research aims at developing mathematically rigorous procedures for physical gauges. The latter are used to calculate basic quantities like self-energies of elementary particles, and to derive nonlocal counterterms in Yang-Mills and Chern-Simons theory at the two-loop level.

During the past two years, emphasis has been on the quantization of non-Abelian gauge theories in the noncovariant Coulomb gauge, which has perplexed theorists for 30 odd years. To solve the problem, a new gauge invariant technique, called split dimensional regularization, was developed, which leads to consistent, ambiguity-free Coulomb-gauge Feynman integrals.

G. Leibbrandt. 1997. Split Dimensional Regularization in the Coulomb Gauge. XXVIII International Conference on High Energy Physics, Warsaw, Poland, July 25-31, 1996. World Scientific, Singapore), Vol. II, 1639-1641.

G. Leibbrandt and J. Williams. 1996. Split Dimensional Regularization for the Coulomb Gauge. Nuclear Physics, B 475, 469-483.

G. Leibbrandt and M. Staley. 1996. QCD Pressure at Two Loops in the Temporal Gauge. Nuclear Physics, B 461, 259-274.

G. Leibbrandt and J.D. Williams. 1995. Two-Loop Quark Self-Energy in a New Formalism (I). Overlapping Divergences. Nuclear Physics, B 440, 573-602.

S. Fachin and G. Leibbrandt. 1995. Technique for Deriving Feynman Integrals in Axial-Type Gauges. International Journal of Modern Physics, A 10, No. 19, 2747-2767.

G. Leibbrandt and M. Staley. 1994. Finite Temperature Calculations in the Temporal Gauge. Nuclear Physics, B 428, 469-484.

G. Leibbrandt and M. Staley. 1994. Debye Screening Length in the Imaginary-Time Formalism in the Temporal Gauge. Proc. Third Workshop on Thermal Field Theories and their Applications, edited by F.C. Khanna, R. Kobes, G. Kunstatter and H. Umezawa (World Scientific Publ. Co. Pte Ltd., Sinapore 1994), pp. 249-254.

G. Leibbrandt and C.P. Martin. 1994. The Light-Cone Gauge, Chern-Simons Theory and Topologically Massive Yang-Mills Theory. Nuclear Physics, B 416, 351-376.

G. Leibbrandt, C.P. Martin and M. Staley. 1993. Nonlocalities in Field Theory. Nuclear Physics, B 405, 777-796. G. Leibbrandt and K. Allan Richardson. 1992. QED in a Unified Axial-Gauge Formalism with a General Gauge Parameter. Physical Review, D 46, 2578-2584.

BOOK:

G. Leibbrandt. 1994. Noncovariant Gauges: Quantization of Yang-Mills and Chern-Simons Theory in Axial-type Gauges. (World Scientific Publishing Co. Pte Ltd., Singapore).