Groups and Manifolds : Lectures for Physicists with Examples in Mathematica /

Groups and Manifolds is an introductory, yet a complete self-contained course on mathematics of symmetry: group theory and differential geometry of symmetric spaces, with a variety of examples for physicists, touching briefly also on super-symmetric field theories. The core of the course is focused...

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Hlavní autoři: Fré, Pietro Giuseppe (Autor), Fedotov, Alexander (Autor)
Médium: E-kniha
Jazyk:angličtina
Vydáno: Berlin ; Boston : De Gruyter, 2017
Edice:De Gruyter Textbook
Témata:
Algebraic topology.
Group theory.
Manifolds (Mathematics)
Differentialgeometrie.
Lie-Algebra.
Supersymmetrie.
SCIENCE / Physics / Mathematical & Computational.
algebrická topológia
diferenciálna geometria
ISBN:9783110551204
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Obsah:
  • Frontmatter
  • Preface
  • Acknowledgement
  • Contents
  • Some remarks about notation
  • 1. Fundamental notions of algebra
  • 2. Groups: a bestiary for beginners
  • 3. Basic elements of finite group theory
  • 4. Finite subgroups of SO(3) and crystallographic groups
  • 5. Manifolds and Lie groups
  • 6. Structure of Lie algebras
  • 7. Root systems and their classification
  • 8. Lie algebra representation theory
  • 9. Exceptional Lie algebras
  • 10. A primary on the theory of connections and metrics
  • 11. Isometries and the geometry of coset manifolds
  • 12. An anthology of group theory physical applications
  • A. Exercises
  • B. MATHEMATICA NoteBooks
  • Bibliography

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