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Quantum field theory III : gauge theory : a bridge between mathematicians and physicists

Author: Eberhard Zeidler
Publisher: Berlin ; New York : Springer, ©2011.
Edition/Format:   Print book : EnglishView all editions and formats

This book examines gauge theory as a tool for describing the fundamental forces acting in the universe: gravitative, electromagnetic, weak interaction and strong interaction. The author used gauge  Read more...


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Document Type: Book
All Authors / Contributors: Eberhard Zeidler
ISBN: 9783642224201 3642224202
OCLC Number: 751804797
Description: xxxii, 1126 pages : illustrations ; 24 cm
Contents: Prologue.- Part I. The Euclidean Manifold as a Paradigm: 1. The Euclidean Space E3 (Hilbert Space and Lie Algebra Structure).- 2. Algebras and Duality (Tensor Algebra, Grassmann Algebra, Cli_ord Algebra, Lie Algebra).- 3. Representations of Symmetries in Mathematics and Physics.- 4. The Euclidean Manifold E3.- 5. The Lie Group U(1) as a Paradigm in Harmonic Analysis and Geometry.- 6. Infinitesimal Rotations and Constraints in Physics.- 7. Rotations, Quaternions, the Universal Covering Group, and the Electron Spin.- 8. Changing Observers - A Glance at Invariant Theory Based on the Principle of the Correct Index Picture.- 9. Applications of Invariant Theory to the Rotation Group.- 10. Temperature Fields on the Euclidean Manifold E3.- 11. Velocity Vector Fields on the Euclidean Manifold E3.- 12. Covector Fields and Cartan's Exterior Differential - the Beauty of Differential Forms.- Part II. Ariadne's Thread in Gauge Theory: 13. The Commutative Weyl U(1)-Gauge Theory and the Electromagnetic Field.- 14. Symmetry Breaking.- 15. The Noncommutative Yang{Mills SU(N)-Gauge Theory.- 16. Cocycles and Observers.- 17. The Axiomatic Geometric Approach to Bundles.- Part III. Einstein's Theory of Special Relativity: 18. Inertial Systems and Einstein's Principle of Special Relativity.- 19. The Relativistic Invariance of the Maxwell Equations.- 20. The Relativistic Invariance of the Dirac Equation and the Electron Spin.- Part IV. Ariadne's Thread in Cohomology: 21. The Language of Exact Sequences.- 22. Electrical Circuits as a Paradigm in Homology and Cohomology.- 23. The Electromagnetic Field and the de Rham Cohomology.- Appendix.- Epilogue.- References.- List of Symbols.- Index
Responsibility: Eberhard Zeidler.


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From the reviews:"This book is the third volume of a complete exposition of the important mathematical methods used in modern quantum field theory. It presents the very basic formalism, important Read more...

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