

HansPeter Künzle
Professor emeritus
Ph.D., University of London
Office: CAB 697
Phone: (780)
4924786
Fax: (780)
4926826
Email: 
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 EinsteinYangMills field equations. Einstein's
gravitation theory and the YangMills 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 spacelike
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 YangMills connections are given, but
rather there are many possible actions which can be classified like
Lie group representations.

[1]
(with Todd A. Oliynyk) Spherical symmetry of generalized
{EYMH} fields, J. Geom. Phys. 56 (2006), 18561874.
(preprint)
[2]
(with Todd A. Oliynyk) On all possible static spherically
symmetric EYM solitons and black holes, Class. Quantum
Grav. 19 (2002), 457482.
[3]
(with Todd A. Oliynyk) Local existence proofs for the boundary
value problem for static spherically symmetric EinsteinYangMills
fields with compact gauge groups, J. Math. Phys. 43
(2002), 23632393.
[4]
(with B.K. Darian) Cosmological EinsteinYangMills
equations, J. Math. Phys. 38 (1997), 46964713. (abstract,preprint)
[5]
Analysis of the static spherically symmetric
SU(n)EinsteinYangMills equations,
Commun. Math. Phys. 162 (1994), 371397. (abstract)
[6]
(with C. Duval) Relativistic and nonrelativistic physical
theories on fivedimensional spacetime, pp. 113129 in
Semantical aspects of spacetime theories (U. Majer and
H.J. Schmidt, eds.), BIWissenschaftsverlag, Mannheim 1994. (abstract) (preprint)
[7]
(with A.K.M. MasoodulAlam) Spherically symmetric static
SU(2) EinsteinYangMills fieoolds, J. Math. Phys. 31
(1990), 928935. (abstract)
[8]
Classical Poincaré and Galilei invariant Hamiltonian
twoparticle interactions with commuting position variables,
Nuovo Cimento B(11) 101 (1988), 721749. (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



