Date: | March 22, 2005 |
The next Johann Bernoulli Lecture will take place on
March 22 2005, 19.30, Akademiegebouw Groningen
The speaker will be:
Jean-Pierre RAMIS, Université Paul Sabatier, Toulouse
The title and summary of his lecture are
FROM LEIBNIZ TO QUANTUM WORLD:
SYMMETRIES, PRINCIPLE OF SUFFICIENT REASON AND AMBIGUITY IN THE SENSE
OF GALOIS
Classical ideas on symmetry mix in fact two related but quite different
things:
1. The notion of group operating on a set.
2. The notion of group of ambiguity in the sense of the last letter of
Evariste Galois.
In the first case, one knows a priori very well the group (formally or
intuitively). In the second case the group is more mysterious but
contains a lot of precious and powerful information.
G. D. Birkhoff and H. Weyl remarked that the symmetry of ambiguity (in
Galois sense) is in fact very similar to some fundamental symmetries of
Physical Theories (like classical mechanics, relativity, classical and
quantum electrodynamics...): "Galois theory is relativity applied to
finite sets". G. D. Birkhoff formulated these ideas in a general
principle valid in mathematics and physics and extending the Principle
of Sufficient Reason of Leibniz.
Today ambiguity groups appear frequently in mathematics and physics and
are extremely powerful tools. After some elementary examples
introducing the idea of symmetry group, I will give an idea of some
recent applications to the old and classical problem of integrability
of dynamical systems (top, three bodies problem, lunar problem...) and
to quantum physics (the Standard Model and the Renormalization in
Quantum Fields Theory). Surprisingly the recent work of A. Connes and
his collaborators about ambiguity groups in quantum fields theory seems
strongly related to very deep questions in arithmetic and we return to
E. Galois last letter.
Last modified: | February 11, 2005 13:40 |