Sample Publications
Invited Talks
Research Group
UofT Physics


The application of modern mathematical methods to the solution of physical problems is fascinating and rewarding. Thus, while the major thrust of my research program is the development of physical theory, I also engage in the development of mathematical methods as they apply to nuclear and other subfields of physics.

The physical problems that intrigue me concern the ways in which the particles of many-body quantum systems interact to produce a variety of highly correlated collective phenomena. I am particularly concerned with developing a microscopic theory of the collective dynamics that take place in nuclear vibrations and rotations and with understanding the nature of the phase transitions that take place with variation of a control parameter.

The atomic nucleus can be viewed as a fluid of nuclear matter, as a gas of interacting neutrons and protons or, at the subnuclear level, as a system of quarks and gluons. Thus, as in other areas of physics, one seeks hierarchies of models and, for a complete understanding, one needs to know how each model relates to the next more microscopic model. By such means one learns how interesting physical phenomena emerge from the interactions and correlated dynamics of its elementary constituents.

My students, colleagues, and I have shown, for example, that the properties of a powerful hydrodynamic model of the nucleus, which exhibits vibrational and rotational dynamics with a variety of possible quantum fluid flows, can be embedded in many-nucleon quantum mechanics. The model can then be derived using the mathematical techniques of analysis by changing the neutron and proton variables to collective and intrinsic variables. It can be understood in geometrical terms, by factoring the multi-dimensional many-nucleon space into products of collective and intrinsic submanifolds, and also by algebraic methods that focus on the symmetries of the model and the expression of its algebra of observables in terms of many-nucleon observables.

It is clear that the above strategy for research has far-reaching applications to many areas of physics that have yet to be explored.

Personal Information  —  back to top

1903-388 Bloor St. East
Toronto, ON
Canada M4W 3W9

Department of Physics
University of Toronto
60 St. George Street
Toronto, ON
Canada M5S 1A7

+1-416-978-5206 office
+1-416-978-7135 secretary
+1-416-967-0413 home

+1-416-978-2537 office


Date of birth
Feb. 4, 1936

British and Canadian

Degrees  —  back to top

B.A. 1959 Cambridge University Mathematics & physics
B.A. 1959 Oxford University
M.A. 1962 Oxford University
D. Phil. 1962 Oxford University Experimental nuclear physics

Employment  —  back to top

Royal Air Force: Lecturer in electronics at an R.A.F. Radio School 1955-56
Niels Bohr Institute, Copenhagen: Ford Foundation Fellow 1962-63
AERE Harwell: U.K.A.E.A. Fellow 1963-66
IAEA Centre for Theoretical Physics, Trieste Visiting Lecturer Oct.- Nov. 1966
University of Rochester: Research Associate 1966-68
University of Toronto: Associate Professor 1968-74
Professor 1974-98
Associate Dean, Physical Sciences, School of Graduate Studies 1984-87
Professor Emeritus 1998-

Chairman IUPAP Commission for Mathematical Physics 1999-2002

Honours  —  back to top

Ford Foundation Fellow, 1962-63
United Kingdom Atomic Energy Authority Fellow l963-66
Alfred P. Sloan Fellow 1970-72
Rutherford Memorial Medal and Prize of the Royal Society of Canada 1983
Erskine Fellow 1984
Fellow, Royal Society of Canada 1986 –
Fellow, Trinity College, University of Toronto 1989 –
Isaac Walton Killam Senior Research Fellow 1990-92
CAP/CRM Medal and Prize for Theoretical and Mathematical Physics 1999

Graduate Students  —  back to top

20 M.Sc. students and 19 Ph.D. students graduated or in progress.

Professional Affiliations  —  back to top

Member, Canadian Association of Physicists.
Member, International Association of Mathematical Physicists.
Fellow, Royal Society of Canada.

Professional Service  —  back to top

  • 1970-71 Chairman, Theoretical Physics Division, C.A.P.
  • 1970-71 Member, Steering Committee for Laurence Report on Support of Physics Research in Universities
  • 1972 Director, Mont Tremblant International Summer School
  • 1972-73 Member, Organizing committee for NATO Advanced Institute on Relativity, Banff, Alberta
  • 1979-82 Member, NSERC Nuclear Physics Grants Selection Committee
  • 1982 Member, International Organizing Committee for the International Symposium on “Time-Dependent Hartree-Fock and Beyond” at Bad-Honnef, Germany.
  • 1983 Member, Special NSERC Committee to evaluate the Major Installation Grant application “Upgrading of Saskatchewan Acceleration Laboratory”.
  • 1983-86 Member, Editorial Board, Physical Review C.
  • 1984 Director, Summer Institute in Theoretical Physics (8-28 July, Kingston, Ont.).
  • 1986 Member, International Advisory Committee for the Conference on “Nuclear Structure, Reactions and Symmetries”, Dubrovnik, May 1986.
  • 1986-92 Member, CAP Committee on Summer Institutes
  • 1986- Review writer for ‘Mathematical Reviews’
  • 1987-8 Member, International Advisory Committee for the XVII’th International Colloquium on Group Theoretical Methods in Physics.
  • 1988-89 Director, Summer Institute in Theoretical Physics (June 26-July 7, 1989, Kingston, Ont.)
  • 1988-93 Member, Editorial Board, Journal of Physics G.
  • 1990 Co-Director, 1990 Summer Institute on Theoretical Physics.
  • 1991 Member, International Advisory Committee, Conference on Group Theory and Special Symmetries in Nuclear Physics, Sept. 19-21, 1991.
  • 1992-93 Deputy Editor, Journal of Physics G.
  • 1992-93 Member, Selection Committee for the Foreign Government Awards and Government of Canada Awards Program.
  • 1994-95 International Advisory Committee for the 1995 Wigner Symposium, Guadalajara, Mexico.
  • 1995-96 International Advisory Committee for the conference “Nuclear Dynamics at Long and Short Distances,” 8 - 12 April, 1996 at Angra dos Reis, Brazil.
  • 1996 -1999 Elected Member, IUPAP Commission for Mathematical Physics.
  • 1998 Director of the Symposium “Impacts of Nuclear Physics” (Toronto, Nov. 23-24).
  • 1999-2002 Elected Chairman, IUPAP Commission for Mathematical Physics.
  • 1999-2001 Member, Selection Committee for the Rutherford Memorial Medal of the R.S.C.
  • 2002 Chairman, Selection Committee for the Rutherford Memorial Medal of the R.S.C.


Sample Publications
Invited Talks
Research Group
UofT Physics