Notre avis :
A compelling study about the link between group theory and geometry by Henri Bacry, an amerit professor of theoretical physics at the Université de la Méditerranée. He is also the Author of many papers in group theory applied to physics (space groups, space-time groups, particle physics groups) and some papers in mathematics.
Résumé :
The Great Bear is apparently composed of seven stars. However one of them is double. We may say that this constellation is made of eight not necessarily distinct stars. Mathematically, we define a constellation of order n as a set of n not necessarily distinct points on a manifold M. From a physical point of view, a pure state of spin s is shown to be a constellation of order 2s on the sphere S, as proved by Majorana. If the 2s points lie on a diameter, the corresponding state is invariant under a rotation around the diameter. There are 2s + 1 ways of putting the 2s points on a diamete. They correspond to the eight states of the angular momentum along the diameter. Mathematically, constellations are objects which have somesthing to do with projective representations of classical groups. Moreover the notion of harmonically conjugate set of points on the sphere is shown to be more simple if we use constellations instead of set of points and harmonically conjugate constellations is defined whatever their order is...
Henri Bacry is an amerit professor of theoretical physics at the Université de la Méditerranée. He is the Author of many papers in group theory applied to physics (space groups, space-time groups, particle physics groups) and some papers in mathematics . He wrote books on physiques, namely, Group theory and particle physics (Gordon and Breach), Localisability and Space in Quantum Physics (Springer-Verlag), Eléments de physique statistique (Ellipses) and a book on symétrie in the large entitled La symétrie dans oous ses états (Vuibert) prefacd by Alain Connes, involvng art, poetry, music architecture, philosophie, science history, etc., for a large public.
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