Lie Groups, Lie Algebras, Cohomology and some Applications in Physics by Jose A. de Azcarraga – A Comprehensive Guide fo

Introduction

For students and researchers venturing into the deeper intersections of mathematics and theoretical physics, Lie Groups, Lie Algebras, Cohomology and some Applications in Physics by Jose A. de Azcarraga offers a rigorous yet accessible pathway. Published by Cambridge University Press, this hardcover volume bridges abstract algebraic concepts with concrete physical phenomena, making it an indispensable resource for anyone working in modern theoretical physics or advanced mathematics.

Book Overview

This self-contained work introduces the cohomology theory of Lie groups and Lie algebras, then systematically explores its profound applications in physics. Starting from foundational ideas in Cartan calculus and differential geometry, the author builds up to sophisticated topics such as fibre bundles, characteristic classes, index theorems, and anomalies. The paperback edition ensures that this essential reference remains affordable for Indian students and libraries.

Key Highlights

• Self-contained approach: Assumes only basic knowledge of differential geometry, with all necessary concepts reviewed in detail.
• Physics-focused applications: Covers monopoles, instantons, supersymmetry, Wess-Zumino-Witten terms, and gauge anomalies.
• Mathematical depth: Includes Chevalley-Eilenberg cohomology, symplectic cohomology, and jet-bundle variational principles.
• Current relevance: Addresses infinite Lie algebras and cohomological descent in mechanics and gauge theories.
• Authoritative publisher: Cambridge University Press ensures high editorial and production standards.

Inside the Book

The text begins with a thorough review of Cartan calculus and the differential geometry of Lie groups. It then moves through fibre bundles and connections, characteristic classes, and index theorems. Later chapters delve into extensions of Lie groups and algebras, supersymmetry applications, and the Chevalley-Eilenberg approach to Lie algebra cohomology. The final sections explore symplectic cohomology, jet-bundle methods in mechanics, Wess-Zumino-Witten terms, and anomalies in gauge theories.

Key Topics

• Differential geometry of Lie groups and Lie algebras
• Fibre bundles, connections, and characteristic classes
• Index theorems and their physical implications
• Monopoles and instantons in gauge theories
• Extensions of Lie groups and algebras
• Supersymmetry and superalgebras
• Chevalley-Eilenberg cohomology
• Symplectic cohomology and variational principles
• Jet-bundle approach to mechanics
• Wess-Zumino-Witten terms
• Infinite-dimensional Lie algebras
• Cohomological descent and anomalies

Reader Benefits

By working through this book, readers gain a unified understanding of how cohomology theory connects abstract algebraic structures to concrete physical models. The numerous examples clarify subtle mathematical points while demonstrating direct utility in problems involving gauge theories, supersymmetry, and topological field theories. The self-contained nature means less time searching for prerequisites and more time focused on core concepts.

Learning Outcomes

After studying this book, readers will be able to apply cohomological methods to analyze Lie group and algebra structures, compute characteristic classes for fibre bundles, understand the geometric origin of anomalies, and use jet-bundle techniques in classical and quantum field theories. They will also be equipped to explore advanced research topics in mathematical physics.

Who Should Read

• Graduate students in theoretical physics and applied mathematics
• Researchers working on gauge theories, supersymmetry, or topological field theories
• Mathematicians interested in applications of Lie theory to physics
• Advanced undergraduates with a background in differential geometry and group theory
• Professionals seeking a comprehensive reference on cohomology in physics

About the Author

Jose A. de Azcarraga is a distinguished theoretical physicist and mathematician with decades of experience in the field. His research spans Lie algebras, superalgebras, cohomology theories, and their applications in particle physics and quantum field theory. He has authored numerous influential papers and books, and his clear exposition makes complex topics accessible to a wide audience.

About the Publisher

Cambridge University Press is one of the world's oldest and most respected academic publishers. Known for its rigorous peer-review process and high-quality production, Cambridge publishes seminal works across all disciplines. This hardcover edition reflects the publisher's commitment to durability and scholarly excellence.

Conclusion

Lie Groups, Lie Algebras, Cohomology and some Applications in Physics is a masterful synthesis of mathematics and physics that belongs on the shelf of every serious student or researcher in these areas. Its clear organization, comprehensive coverage, and focus on physical applications make it an enduring reference. Order your copy today from Bookshops.in and deepen your understanding of the geometric and algebraic foundations of modern physics.