Group theory [electronic resource] : application to the physics of condensed matter / M.S. Dresselhaus, G. Dresselhaus, A. Jorio.

Includes bibliographical references (pages 549-552) and index

Basic mathematical background: introduction -- representation theory and basic theorems -- Character of a representation -- Basic functions -- Splitting of atomic orbitals in a crystal potential -- Application to selection rules and direct products -- Electronic states of molecules and directed valence -- Molecular vibrations, infrared, and Raman activity -- Space groups in periodic lattices -- Space groups in reciprocal space and representations -- Applications to lattice vibrations -- Electronic energy levels in a cubic crystals --Energy band models based on symmetry -- Spin-orbit interaction in solids and double groups -- Applications of double groups to energy bands with spin -- Time reversal symmetry -- Permutation groups and many-electron states -- Symmetry properties of tensors.

"Every process in physics is governed by selection rules that are the consequence of symmetry requirements. The beauty and strength of group theory resides in the transformation of many complex symmetry operations into a very simple linear algebra, this concise and class-tested-book has been pedagogically tailored over 30 years at MIT and 2 years at the University Federal of Minas Gerais (UFMG) in Brazil. The approach centers on the conviction that teaching group theory in close connection with applications helps students to learn; understand and use it for their own needs. For this reason, the theoretical background is confined to the first 4 introductory chapters (6-8 classroom hours)." "From there, each: chapter develops new theory while introducing applications so that the students can best retain new concepts, build on concepts learned the previous week, and see interrelations between topics as presented. Essential problem sets between the chapters also aid the retention of the new material and for the consolidation of material learned in previous chapters. The text and problem sets have proved a, useful springboard for the application of the basic material presented here to topics in semiconductor physics and the physics of carbon-based nanostructures."--Jacket.