Quaecumque VeraDepartment of Mathematical and
Statistical Sciences
Hans-Peter Künzle
    Hans-Peter Künzle
Professor emeritus
Ph.D., University of London

Office: CAB 697
Phone: (780) 492-4786
Fax: (780) 492-6826

Research Interests
My research interests are in application of differential geometrical methods to general relativity, classical field theories and classical mechanics. I have worked on Lagrangian formulations of classical field theories, in particular, Einstein's general relativity and the transition to the Newtonian Limit. Similarly I have investigated the relation between Hamiltonian multiparticle systems in a symplectic formulation with relativistic, i.e. Poincaré invariant formulations.

Within Einstein's General Relativity Theory proper I investigated asymptotically Euclidean static and stationary perfect fluid models and made some contributions towards a proof that they must be spherically symmetric in the static case and have unique slightly ellipsoidal configurations for small angular velocity, the configuration depending only on the equation of state, the total mass and the angular momentum.

For the last about ten years I have concentrated on classical solutions of the Einstein-Yang-Mills field equations. Einstein's gravitation theory and the Yang-Mills gauge theories describe the most fundamental forces of physics. Both theories will have to be quantized for the most precise description of nature, but also investigating the classical field equations is most interesting.

I am now looking at finding analytical and numerical solutions for systems with a very high symmetry, like static ones with spherical symmetry and cosmological solutions with homogeneous space-like sections. Such models are also particularly interesting mathematically because there is no natural action of the symmetry group on the principal bundle on which the Yang-Mills connections are given, but rather there are many possible actions which can be classified like Lie group representations.

Selected Publications

[1] (with Todd A. Oliynyk) Spherical symmetry of generalized {EYMH} fields, J. Geom. Phys. 56 (2006), 1856-1874. (preprint)

[2] (with Todd A. Oliynyk) On all possible static spherically symmetric EYM solitons and black holes, Class. Quantum Grav. 19 (2002), 457-482.

[3] (with Todd A. Oliynyk) Local existence proofs for the boundary value problem for static spherically symmetric Einstein-Yang-Mills fields with compact gauge groups, J. Math. Phys. 43 (2002), 2363-2393.

[4] (with B.K. Darian) Cosmological Einstein-Yang-Mills equations, J. Math. Phys. 38 (1997), 4696-4713. (abstract,preprint)

[5] Analysis of the static spherically symmetric SU(n)-Einstein-Yang-Mills equations, Commun. Math. Phys. 162 (1994), 371-397. (abstract)

[6] (with C. Duval) Relativistic and nonrelativistic physical theories on five-dimensional space-time, pp. 113-129 in Semantical aspects of spacetime theories (U. Majer and H.-J. Schmidt, eds.), BI-Wissenschaftsverlag, Mannheim 1994. (abstract) (preprint)

[7] (with A.K.M. Masood-ul-Alam) Spherically symmetric static SU(2) Einstein-Yang-Mills fieoolds, J. Math. Phys. 31 (1990), 928-935. (abstract)

[8] Classical Poincaré and Galilei invariant Hamiltonian two-particle interactions with commuting position variables, Nuovo Cimento B(11) 101 (1988), 721-749. (abstract)

Department of Mathematical and Statistical Sciences
University of Alberta
632 Central Academic Building
Edmonton, AB T6G 2G1
Phone: 780.492.3396
Fax: 780.492.6826
Last modified 26.09.06

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