A Physicist's Introduction to Algebraic Structures
A Physicist's Introduction to Algebraic Structures
An algebraic structure consists of a set of elements, with some rule of combining them, or some special property of selected subsets of the entire set. Many algebraic structures, such as vector space and group, come to everyday use of a modern physicist. Catering to the needs of graduate students and researchers in the field of mathematical physics and theoretical physics, this comprehensive and valuable text discusses the essential concepts of algebraic structures such as metric space, group, modular numbers, algebraic integers, field, vector space, Boolean algebra, measure space and Lebesgue integral. Important topics including finite and infinite dimensional vector spaces, finite groups and their representations, unitary groups and their representations and representations of the Lorentz group, homotopy and homology of topological spaces are covered extensively. Rich pedagogy includes various problems interspersed throughout the book for better understanding of concepts.
- Includes detailed proofs of important theorems
- Offers more than 400 problems to test the understanding of concepts, including answers to many of them
- In-depth coverage of topics includes vector space, group, and topological space
- Topology is introduced after group theory, helping students understand the topological properties of group parameter spaces
Product details
February 2025Paperback
9781108729116
550 pages
228 × 152 mm
Not yet published - available from February 2025
Table of Contents
- Preface
- Part I. General Introduction:
- 1. Rules of logic
- 2. Sets and functions
- 3. Algebraic structures
- Part II. Vector Spaces:
- 4. Basics
- 5. Operators on vector spaces
- 6. Infinite dimensional vector spaces
- Part III. Group Theory:
- 7. General properties of groups
- 8. Finite groups
- 9. Representation of finite groups
- 10. Symmetries of regular geometrical objects
- 11. Countably infinite groups
- 12. General properties of Lie groups
- 13. Rotations and translations
- 14. Unitary groups and their representations
- 15. Orthogonal groups and their representations
- 16. Parameter space of Lie groups
- 17. Representations of the Lorentz group
- 18. Roots and weights
- 19. Some other groups and algebras
- Part IV. Topology:
- 20. Continuity of functions
- 21. Topological spaces
- 22. Homotopy theory
- 23. Homology
- Appendices
- References
- Index.
