# Ian Affleck, Professor

B.Sc., Trent (75); A.M., Ph.D., Harvard (76,79)
Junior Fellow, Harv. Soc. of Fellows (79-81)
Asst. Prof., Princeton (81-87)
Researcher, CEN-Saclay, France (84-85)
Steacie Prize (88)
A.P. Sloan Found. Fellow (83-87)
CIAR Fellow (87-), Hertzberg Medal (90), Rutherford Medal (91)
Killam Prize (92), Biely Prize (92), F.R.S.C.

## Research Interests

My current research is at the interface between elementary particle
theory and condensed matter theory. Elementary particle theory has
developed many fascinating mathematical constructions such as string
theory, which are often difficult to apply directly to the present-day
experimental reality of particle physics. Condensed matter physics
offers a host of exotic experimental systems which can sometimes provide
applications for these sophisticated mathematical ideas.
I mention three examples:

A major challenge at present in condensed matter
theory is to understand the new high-Tc superconductors.

Quasi-one dimensional antiferromagnets studied, for example, by
neutron-scattering at Chalk River, Ontario. These provide experimental
applications of quantum field theory in one space and one time
dimension.

The technique of conformal field theory, which is the mathematical
underpinning of string theory, has been recently developed to discover
new aspects of possible interactions between magnetic impurities and
conduction electrons in metals.

## Selected Publications

"Field Theory Methods and Quantum Critical Phenomena", Fields, Strings
and Critical Phenomena, p. 563-640 (ed. E. Brezin and J. Zinn-Justin
North Holland, Amsterdam, 1990), I. Affleck.
"Critical Theory of Overscreened Kondo Fixed Points", Nucl. Phys. B360,
641-696 (1991), I. Affleck and A.W.W. Ludwig.

"Bose Condensation in Quasi-one-dimensional Antiferromagnets in Strong
Fields", Phys. Rev. B43, 3215-3222 (1991), I. Affleck.

"Universal Non-Integer Groundstate Degeneracy in Critical Quantum
Systems", Phys. Rev. Lett., 67, 161-164 (1991), I. Affleck and A.W.W.
Ludwig.

"Exact Critical Theory of the Two Impurity Kondo Model", Phys.Rev.Lett.,
68, 1046-1050 (1992), I. Affleck and A.W.W. Ludwig.

"Longitudinal Modes in Haldane Gap Antiferromagnets", Phys. Rev. B46,
8934-8953 (1992), I. Affleck and G.F. Wellman.