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Group Theoretical Methods and Applications to Molecules and Crystals


  • Date Published: September 2005
  • availability: Available
  • format: Paperback
  • isbn: 9780521020381

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About the Authors
  • This book explains the basic aspects of symmetry groups as applied to problems in physics and chemistry using an approach pioneered and developed by the author. The symmetry groups and their representations are worked out explicitly, eliminating the undue abstract nature of group theoretical methods. The author has systemized the wealth of knowledge on symmetry groups that has accumulated in the century since Fedrov discovered the 230 space groups. All space groups, unitary as well as antiunitary, are reconstructed based on the algebraic defining relations of the point groups. This work will be of great interest to graduate students and professionals in solid state physics, chemistry, mathematics, geology and those who are interested in magnetic crystal structures.

    • The author is well known as the main figure in the development of this work
    • This work is important in many areas of condensed matter physics and solid state/physical chemistry
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    Reviews & endorsements

    'The author's unique approach and methods which are developed in this book to discuss space groups and their matrix representations, try to overcome the abstract nature of the classical group theoretical methods. In this perspective, and as illustrated in this monograph, this work aims to close the gap between the abstract mathematical theory of space groups and its concrete applications in other sciences.' Wim Malfait, Zentralblatt für Mathematik

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    Product details

    • Date Published: September 2005
    • format: Paperback
    • isbn: 9780521020381
    • length: 512 pages
    • dimensions: 244 x 170 x 26 mm
    • weight: 0.796kg
    • contains: 69 b/w illus. 41 tables
    • availability: Available
  • Table of Contents

    List of symbols
    1. Linear transformations
    2. Theory of matrix transformations
    3. Elements of abstract group theory
    4. Unitary and orthogonal groups
    5. The point groups of finite order
    6. Theory of group representations
    7. Construction of symmetry adapted linear combinations based on the correspondence theorem
    8. Subduced and induced representations
    9. Elements of continuous groups
    10. The representations of the rotation group
    11. Single- and double-valued representations of point groups
    12. Projective representations
    13. 230 space groups
    14. The representations of space groups
    15. The unirreps of the space groups to energy bands and vibrational modes of crystals
    16. Time reversal, antiunitary point groups and their core presentations
    17. Antiunitary space groups and their core presentations
    Appendix. Character tables for the crystal point groups

  • Author

    Shoon K. Kim, Temple University, Philadelphia

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