Geometry and Quantum Features of Special Relativity
Description
This second edition of "The Geometry of Special Relativity - a Concise Course" offers more than just corrections and enhancements. It includes a new chapter on four-velocities and boosts as points and straight lines of hyperbolic geometry. Quantum properties of relativistic particles are derived from the unitary representations of the Poincaré group. Notably, the massless representation is related to the concept of a Hopf bundle. Scattering theory is developed analogously to the non-relativistic case, relying on proper symmetry postulates. Chapters on quantum fields, reflections of charge, space, and time, and the necessary gauge symmetry of quantized vector fields complete the foundation for evaluating Feynman graphs. An extended appendix covers more than a dozen additional topics.
The first half of this edition refines the first edition, using simple diagrams to explain time dilation, length contraction, and Lorentz transformations based on the invariance of the speed of light. The text derives key results of relativistic physics and resolves apparent paradoxes. Following a presentation of the action principle, Noether's theorem, and relativistic mechanics, the book covers the covariant formulation of electrodynamics and classical field theory. The groups of rotations and Lorentz transformations are also examined as a transition to relativistic quantum physics.
This text is aimed at graduate students of physics and mathematics seeking an advanced introduction to special relativity and related topics. Its presentation of quantum physics aims to inspire fellow researchers.
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Norbert Dragon is a retired Professor of Theoretical Physics at Leibniz University Hannover in Germany. He studied Physics at Technische Hochschule Karlsruhe, where he completed his PhD under Julius Wess in 1977. These were the years when Wess and Zumino were establishing and expanding Supersymmetry and Supergravity. Among his fellow students at the same institute were Martin Sohnius, Richard Grimm, Klaus Sibold, and Hermann Nicolai.
He worked as an assistant to Berthold Stech at Universität Heidelberg from 1979 to 1986. Since 1988, he has been a Professor at the Institut für Theoretische Physik at Universität Hannover. He retired in 2016.
He enjoyed teaching beginners as much as he did teaching PhD students, covering advanced topics such as Supersymmetry and BRST-symmetry, to which he has contributed research papers. In his teaching, he aimed to find everyday examples for abstract mathematical concepts. For instance, a shopping list and commodity prices exemplify high-dimensional vector spaces and their duals. Similarly, holes in trousers and patches of cloth have areas of opposite signs because the areas cancel out when mending holes. Thus, the concept of positive and negative areas becomes commonplace and comprehensible.
Content
Structures of Spacetime.- Time and Distance.- Transformations.- Relativistic Particles.- Electrodynamics.- Classical Field Theory.- The Lorentz Group.-Hyperbolic and Spherical Geometry.- Relativistic Quantum Physics.- Scattering.- Quantum Fields.- Space Inversion, Time Reversal, Charge Conjugation.- Gauge Symmetry.- Appendix A, B, C, D.- References.- Index.