Department of Analysis und Mathematical Physics
Research 1993-95
Project:
Nonstandard Analysis in Operator Theory and Mathematical Physics
Participants:
HONEGGER, R. (Dr.rer.nat., Institut für Theoret. Physik)
RÄBIGER, F. (Universitätsdozent Dr.rer.nat.,
Arbeitsbereich Funktionalanalysis)
WOLFF, M.
(Prof. Dr.rer.nat.)
together with:
ALBEVERIO, S.A. (Prof.Dr., Fachbereich Mathematik, Univ. Bochum)
LUXEMBURG, W.A.J. (Prof., Dept. of Mathem.,
California Institute of Technology, Pasadena, Ca, USA)
WERNER, R. (Dozent Dr.rer.nat., Univ. Osnabrück)
Text:
In treating very complex problems of quantum theory and mathematical physics
often one encounters difficult limiting procedures which may be solved especially easy
(and in most cases for the first time) by methods of nonstandard analysis.
This includes questions of stability of one-parameter semigroups of linear
operators as well as questions concerning intensive variables or fluctuations
in quantum lattice models or the question for the "limit" of quantum mechanics
for h ->
0. In all of these problems the possibility to treat "infinitely small"
and "infinitely large" quantities in a mathematically rigorous way using
nonstandard analysis leads to new insights and solutions.
DFG
Key Publication:
Albeverio, S.A., Luxemburg, J., Wolff, M.P.H. (eds.):
Advances in Analysis, Probability and Mathematical Physics -
Contributions of Nonstandard Analysis,
Kluwer Acad. Publ. Dordrecht 1995, xi + 251 pp.
Rolf Gohm
rolf.gohm@uni-tuebingen.de