| dc.description.abstract | Symmetry can be seen as the most basic and important concept in physics.
Momentum conservation is a consequence of translational symmetry of space.
More generally, every process in physics is governed by selection rules that
are the consequence of symmetry requirements. On a given physical system,
the eigenstate properties and the degeneracy of eigenvalues are governed by
symmetry considerations. The beauty and strength of group theory applied to
physics resides in the transformation of many complex symmetry operations
into a very simple linear algebra. The concept of representation, connecting
the symmetry aspects to matrices and basis functions, together with a few
simple theorems, leads to the determination and understanding of the fundamental
properties of the physical system, and any kind of physical property,
its transformations due to interactions or phase transitions, are described in
terms of the simple concept of symmetry changes.
The reader may feel encouraged when we say group theory is “simple linear
algebra.” It is true that group theory may look complex when either the mathematical
aspects are presented with no clear and direct correlation to applications
in physics, or when the applications are made with no clear presentation
of the background. The contact with group theory in these terms usually leads
to frustration, and although the reader can understand the specific treatment,
he (she) is unable to apply the knowledge to other systems of interest. What
this book is about is teaching group theory in close connection to applications,
so that students can learn, understand, and use it for their own needs. | en_US |
