Shattered Symmetry: Group Theory from the Eightfold Way to the Periodic Table

ISBN : 9780190611392

Arnout Ceulemans; Pieter Thyssen
528 ページ
156 x 235 mm

The standard model of subatomic particles and the periodic table of the atoms have the common goal to bring order in the bewildering chaos of the constituents of matter. Their success relies on the presence of fundamental symmetries in their core. The purpose of the book is to share the admiration for the power and the beauty of these symmetries. The reader is taken on a journey from the basic geometric symmetry group of a circle to the sublime dynamic symmetries that govern the motions of the particles. The trail follows the lines of parentage linking groups upstream to the unitary symmetry of the eightfold way of quarks, and to the four-dimensional symmetry of the hydrogen atom. Along the way the theory of symmetry groups is gradually introduced with special emphasis on graphical representations. The final challenge is to open up the structure of Mendeleev's table which goes beyond the symmetry of the hydrogen atom. Breaking this symmetry to accommodate the multi-electron atoms requires to leave the common ground of linear algebras and explore the potential of non-linearity.


1. A primer on symmetry
2. The elements of group theory
3. The axial rotation group
4. The SO(2) group
5. The SO(3) group
6. Scholium I
7. The SU(3) group
8. SU(2) and electron spin
9. The SO(4) group
10. Scholium II
11. The SO(2,1) group
12. The SO(4,2) group
13. The periodic table
14. SO(4,2) and the rules of atomic chess


Arnout Ceulemans is Full Professor of Theoretical Chemistry at the University of Leuven in the Faculty of Science. His research is devoted to the development and application of group theory and topology to chemistry.; Pieter Thyssen is a Postdoctoral Researcher in the Department of Chemistry at the Catholic University of Leuven. He completed his PhD at Leuven in 2013 under the supervision of Arnout Ceulemans.