Symmetry in Physics
In the Oxford Dictionary of Current English symmetry is defined as the "right correspondence of parts; quality of harmony or balance (in size, design etc.) between parts". The word symmetry is derived from Greek where it has the meaning "with proportion" or "with order". In modern theories of physics it has acquired a more precise meaning but the general idea of seeking to order physical phenomena still remains. Confronted with the bewildering complexity exhibited by the a multitude of physical systems, physicists attempt to extract some simple regularities from observations, and the fact that they can do so is largely due to the presence of symmetries in the laws of physics. Although one can never hope to explain all observational complexities entirely on the basis of symmetry arguments only, these are nevertheless instrumental in establishing correlations between and (hidden) regularities in the data.
The mathematical theory of symmetry is called group theory and its origin dates back to the beginning of the nineteenth century. Of course, the notion of symmetry is present implicitly in many mathematical studies that predate the birth of group theory and goes back even to the ancient Greeks, in particular Euclid. It is, however, Evariste Galois who perceived the importance of the group of permutations to answer the question whether the roots of a polynomial equation can be algebraically represented or not. In the process of solving that long-standing mathematical problem he invented group theory as well as Galois theory which is an investigation of the relation between polynomials and groups. The mathematical theory of groups did develop throughout the entire nineteenth century and made another leap forward in 1873 when Sophus Lie proposed the concept of a Lie group.
These pages give an overview of my current research interests. Since most of the time I view physics from a symmetry angle, I have collected everything under the heading "symmetry in physics". However, it should be clear that no exhaustive overview of the topic is intended here. Rather, examples are given of applications of symmetry to quantal many-body systems (mostly, but not exclusively, atomic nuclei) which have caught my interest recently.
Contact: P. Van Isacker