The Mathematical Foundations of Gauge Theories
Published in June 1992
Book
Hardback
394 pages
978-0-444-89708-4 (ISBN)
Description
Theoretical physicists tend to discuss their theories in the language of mathematics. However, the adequate mathematical formulation may not yet be available when the physical law is first discovered. Mathematical physicists trying to develop the relevant mathematics for these theories, may obtain new insights into old mathematical structures or may even disclose entirely new structures. Gauge Theory is such a gift from physics to mathematics. This volume presents a self-contained development of a differential geometric formulation of gauge theories, in particular, the theory of Yang-Mills fields. The book is aimed at advanced graduate students and research workers in theoretical physics and pure and applied mathematics who are acquainted with the elements of the theory of differential manifolds. It enables the reader to apply this theory to gauge theories and to understand the role of gauge theories in high energy physics, gravitation theory and electromagnetism.
Theoretical physicists tend to discuss their theories in the language of mathematics. However, the adequate mathematical formulation may not yet be available when the physical law is first discovered. Mathematical physicists trying to develop the relevant mathematics for these theories, may obtain new insights into old mathematical structures or may even disclose entirely new structures. Gauge Theory is such a gift from physics to mathematics. This volume presents a self-contained development of a differential geometric formulation of gauge theories, in particular, the theory of Yang-Mills fields. The book is aimed at advanced graduate students and research workers in theoretical physics and pure and applied mathematics who are acquainted with the elements of the theory of differential manifolds. It enables the reader to apply this theory to gauge theories and to understand the role of gauge theories in high energy physics, gravitation theory and electromagnetism.
Theoretical physicists tend to discuss their theories in the language of mathematics. However, the adequate mathematical formulation may not yet be available when the physical law is first discovered. Mathematical physicists trying to develop the relevant mathematics for these theories, may obtain new insights into old mathematical structures or may even disclose entirely new structures. Gauge Theory is such a gift from physics to mathematics. This volume presents a self-contained development of a differential geometric formulation of gauge theories, in particular, the theory of Yang-Mills fields. The book is aimed at advanced graduate students and research workers in theoretical physics and pure and applied mathematics who are acquainted with the elements of the theory of differential manifolds. It enables the reader to apply this theory to gauge theories and to understand the role of gauge theories in high energy physics, gravitation theory and electromagnetism.
More details
Series
Language
English
Place of publication
Oxford
United Kingdom
Publishing group
Elsevier Science & Technology
Target group
College/higher education
Professional and scholarly
Dimensions
Height: 230 mm
ISBN-13
978-0-444-89708-4 (9780444897084)
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Schweitzer Classification
Content
Preface. 1. Elements of differential geometry. 2. Principal and associated bundles. 3. Theory of connections. 4. Algebraic topology of manifolds. 5. Characteristic classes. 6. Theory of gauge fields. 7. Associated fields. 8. Yang-Mills fields. 9. Instantons and their moduli spaces. 10. Yang-Mills-Higgs Fields. 11. Quantization of gauge fields. A. Dictionary of terminology. B. Point set topology. C. Categories and functors. D. Chain complexes. E. Clifford algebras. Bibliography. Glossary. Index.