Mark Walton
 Faculty
 Physics and Astronomy
 Office: SA9334
 Phone: (403) 3292357
 Research
 Room: SA8336
 Phone: (403) 3292357
Degrees
B.Sc. (Hons.) (Physics); M.Sc., Ph.D. (Theoretical HighEnergy Physics)Expertise
Mathematical physics, quantum theory, particle physics theory, Lie algebras and groups in physicsResearch Areas
Quantum mechanics: emergence of classical mechanics in quantum phase space, quantization, open quantum systems, and foundations of quantum theory, Conformal field theory: algebraic and combinatorial structures, and possible stringtheory applications, Lie algebras and groups and their physical applicationsAlternate Languages
FrenchBiography
Mark is a professor in the Department of Physics and Astronomy. He has been a faculty member since January 1991. Prof. Walton is a theoretical and mathematical physicist. His B.Sc. (Honours) is from Dalhousie University in Halifax, and his M.Sc and Ph.D. (1987) were both completed at McGill University in Montreal. Mark's M.Sc. research was in elementary particle physics (or high energy physics) and his Ph.D. research was in string theory. During an NSERC Postdoctoral Fellowship at the Stanford Linear Accelerator Center he switched research fields to conformal field theory and related topics (a fairly nontechnical introduction to conformal field theory is: J. Cardy, Physics World, June, 1993, pg 29). His 2nd postdoctoral position, at Université Laval, was shortened when he was offered the faculty position here at the U of L. In recent years, Prof. Walton has been studying quantum mechanics, and in particular, its phasespace formulation. Mark is interested in how classical mechanics emerges from quantum theory, and in the foundations of quantum mechanics. Throughout his research career, Prof. Walton has applied the math of Lie groups and algebras to various physical systems.Selected Publications
B. Belchev*, S.G. Neale*, M.A. Walton, Flow of Smatrix Poles for Elementary Potentials, accepted 8/11 by the Canadian Journal of PhysicsB. Belchev*, M.A. Walton, Solving for the Wigner Functions of the Morse Potential, J. Phys. A: Math.Theor. 43 (2010) 225206
B. Belchev*, M.A. Walton, On Robin Boundary Conditions and the Morse Potential in Quantum Mechanics, J. Phys. A: Math.Theor. 43 (2010) 085301
B. Belchev*, M.A. Walton, On Wigner Functions and a Damped Star Product in Dissipative Phasespace Quantum Mechanics, Ann. Phys. 324 (2009) 670
N. Okeke*, M.A. Walton, On Character Generators for Simple Lie Algebras, J. Phys. A: Math.Theor. 40 (2007) 8873
*students
Research Interests
Conformal Field Theory & PhaseSpace Quantum MechanicsFields describe an enormous range of phenomena in physics. The predictions of a field theory are often difficult to work out, however, unless a system can be described as a small perturbation of another wellunderstood one. Some field theories do exist, however, that can be solved nonperturbatively. Conformal (quantum) field theories (CFTs) are examples. I study them because I believe they will teach us something to help us solve other physical theories. Happily, CFTs also find many uses, in statistical physics and condensed matter physics, for examples. My research focuses on improving the understanding of their mathematical properties, so that their predictions can be worked out, and new applications can be found.
Quantum field theory (QFT) is consistent with all experiments performed to date. It treats the elementary particles as structureless points. In spite of enormous effort, however, a QFT of gravity has not been constructed. String theory posits that the elementary particles are not pointlike, but tiny strings, so small that their structure has not yet been detected. The payoff is that string theory can describe a unified theory of forces, including quantum gravity.
CFT also applies to string theory. Strings sweep out a twodimensional world sheet in spacetime, and CFT describes the physics on the string world sheet. Part of my research focuses on the application of CFT to the study of string theory. I am also interested in the mathematics of CFT, for example, the infinitedimensional affine KacMoody algebras and the semisimple Lie algebras they are based on that are important in CFT.
A second important line of research deals with a different way of doing quantum mechanics, known as phasespace quantum mechanics (or deformation quantization, or WignerWeyl quantization, among other names). In it, observables are not represented by operators, but rather as ordinary functions on phase space. That way, connections with classical mechanics are often most transparent. For several years now, I have studied the phasespace quantization of simple systems that have unusual or difficult quantum aspects. They include the damped harmonic oscillator, boundaries in phase space, and point interactions. The goal is to deepen our understanding of these systems by looking at them from this new, different point of view.
Current Research and Creative Activity
Title  Location  Grant Information  Principal Investigator  Co Researchers 

Conformal field theory, star quantization, and matrix models, for physical applications 
Natural Sciences and Engineering Research Council (NSERC), $40,000/year for 5 years, 200611.

M.A. Walton, University of Lethbridge 
Previous Research
Title  Grant Agency  Completion Date 

Conformal field theory with applications to string theory  Natural Sciences and Engineering Research Council (NSERC)  2006 
Conformal field theory  Natural Sciences and Engineering Research Council (NSERC)  2002 
Conformal field theory and related systems  Natural Sciences and Engineering Research Council (NSERC)  1999 