2006 NSERC Steacie Fellow Andrzej Czarnecki

Physicists count on the numbers man

The barnyard of subatomic particles that has been assembled by physics over the course of the past century includes the smallest, lightest things in the known universe. Yet making sense of their behaviour calls for some very heavy lifting, involving computational techniques at the frontier of contemporary mathematics.

Just ask Andrzej Czarnecki, a University of Alberta physicist who has been exploring this frontier for more than a decade. He has mapped out new methods for handling the very difficult calculations associated with quantum electrodynamics and quantum chromodynamics, disciplines that call for a formal interpretation of the motions and light emissions observed in particle accelerators around the world.

“I view much of my work as a service to people who like very challenging experiments,” says Dr. Czarnecki, referring to the intricate collisions that create, destroy, or otherwise manipulate various members of this stable of particles. It may be all too easy to think of these activities as tiny billiard balls running into one another, but the reality is much more dazzling. Energy is exchanged in some downright peculiar ways, often creating forms of matter that defy explanation.

The task set for Dr. Czarnecki and his colleagues is to provide that explanation. More specifically, they tackle a set of daunting equations known as perturbation expansions, which provide numerical details to accompany the findings of quantum physics.

“Brute force methods often fail, because errors accumulate,” he says, pointing out that simply running numbers through ever more powerful computers will not necessarily yield a good answer. Instead, Dr. Czarnecki has established the Centre for Symbolic Computation, a set of computer clusters that run a variety of innovative software tools, algorithms carrying out calculations based on symbols rather than numerical entries.

“We don’t crunch numbers,” he explains, noting that this approach eliminates the need to truncate calculations at some point, a practical matter that can nevertheless magnify the limitations of an experiment. “We manipulate formulas. These are algebraic manipulations. It doesn’t mean our calculations are absolutely accurate, but we don’t suffer from truncation errors. We can use different approximation schemes using symbolic computation, and this gives more insight into the physics of some phenomena.”

As one of six 2006 NSERC Steacie Fellows, Dr. Czarnecki intends to focus on one of the more tantalizing examples of such phenomena, a curiosity surrounding the energy levels of electrons in the hydrogen atom. Called the Lamb Shift, it refers to a discrepancy between the levels that would be expected from quantum mechanics and the spectrographic pattern that is actually seen in the laboratory.

First observed in the 1940s, the effect provides a window into the intricate self-interactions of electrons. The quest to better understand this behaviour is spawning a collaboration of high-energy and atomic theorists, who are trying to clarify important distinctions between such behaviour in free-flying particles and in those “bound” to an atom.

“For a long time there was a bit of a mystery surrounding these bound states,” he says. “The methods from high-energy physics that we applied to such problems have helped to demystify them. Now we are poised to bring the theory of atomic transitions to a new level of precision and make predictions for the new round of spectroscopy experiments.”