A Physicist's Introduction to Algebraic Structures
Vector Spaces, Groups, Topological Spaces and More
Published on 23. May 2019
Book
Hardback
712 pages
978-1-108-49220-1 (ISBN)
Description
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.
More details
Language
English
Place of publication
Cambridge
United Kingdom
Target group
Professional and scholarly
Illustrations
Worked examples or Exercises
Dimensions
Height: 260 mm
Width: 208 mm
Thickness: 43 mm
Weight
1735 gr
ISBN-13
978-1-108-49220-1 (9781108492201)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
Palash B. Pal
A Physicist's Introduction to Algebraic Structures
Vector Spaces, Groups, Topological Spaces and More
Book
approx. 05/2026
Cambridge University Press
€83.50
Not yet published
Palash B. Pal
A Physicist's Introduction to Algebraic Structures
Vector Spaces, Groups, Topological Spaces and More
E-Book
05/2019
Cambridge University Press
€113.99
Available for download
Person
Palash B. Pal is Senior Professor in the Theory Division at the Saha Institute of Nuclear Physics, Kolkata. His current research includes elementary particle physics, with specializations in neutrinos, grand unified theories, and particles in electromagnetic fields. He has published more than 100 papers in journals of international repute. He has taught courses on mathematical methods, particle physics, quantum field theory, theoretical physics and classical field theory at graduate level. He carried out postdoctoral research at the University of Maryland, University of Massachusetts, University of Oregon and University of Texas.
Content
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.