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Symmetries in Fundamental Physics


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Table of Contents

Preface.- Notation.- Introduction.- Symmetry: Argument, Principle, and Leitmotif.- Operations and Invariants.- "Symmetries" in "Fundamental Physics".- The Scope of Symmetries.- Bibliographical Notes.- Classical Mechanics.- Newtonian and Analytical Mechanics.- Symmetries and Conservation Laws.- Galilei Group.- Electrodynamics and Special Relativity.- Electrodynamics a la Maxwell.- Special Relativity.- Noether Theorems.- Poincare Transformations.- Generalizations of Poincare Symmetry.- On the Validity of Special Relativity.- Quantum Mechanics.- Principles of Quantum Mechanics.- Symmetry Transformations in Quantum Mechanics.- Quantum Physics and Group Representation.- Relativistic Field Theory.- Representations of the Poincare Group.- Symmetry and Quantum Field Theory.- Actions.- Spontaneous Symmetry Breaking.- Discrete Symmetries.- Effective field theories.- Particle Physics.- Particles and Interactions.- Strong Interactions.- Weak and Electromagnetic Interaction.- Paralipomena on the Standard Model.- General Relativity and Gravitation.- Introductory Remarks.- Equivalence Principle.- Riemann-Cartan Geometry.- Physics in Curved Spacetime.- Geometrodynamics.- Modifications and Extensions of/to General Relativity.- Unified Field Theories.- Grand Unified Theories.- Kaluza-Klein Theory.- Supersymmetry.- Further Speculations.- Conclusion.- Symmetries: The Road to Reality.- Are Symmetries a Principle of Nature?.- Physics Beyond Symmetries.- Appendices.- A Group Theory.- B Spinors, Z2-gradings, and Supergeometry.- C Symmetries and Constrained Dynamics.- D Symmetries in Path-Integral and BRST Quantization.- E Differential Geometry.- F Symmetries in Terms of Differential Forms.- Bibliography.


From the book reviews:

"The material is very well organized, clean and easy to find. And contains a lot of useful content. ... this is an excellent book that can become a formidable companion for a student or for a researcher. There is a lot of stuff here, explained in a very clean way. Very good job, Prof. Sundermeyer!" (Giuseppe Nardelli, Mathematical Reviews, October, 2014)

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