Authors:
- Mathematically rigorous treatment of special relativity with precise statement of the physical interpretation
- Detailed introduction to the the theory of spinors in Minkowski spacetime
- Thorough treatments of numerous topics not generally discussed at the introductory level
Part of the book series: Applied Mathematical Sciences (AMS, volume 92)
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Table of contents (5 chapters)
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Front Matter
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Back Matter
About this book
This book offers a presentation of the special theory of relativity that is mathematically rigorous and yet spells out in considerable detail the physical significance of the mathematics. It treats, in addition to the usual menu of topics one is accustomed to finding in introductions to special relativity, a wide variety of results of more contemporary origin. These include Zeeman’s characterization of the causal automorphisms of Minkowski spacetime, the Penrose theorem on the apparent shape of a relativistically moving sphere, a detailed introduction to the theory of spinors, a Petrov-type classification of electromagnetic fields in both tensor and spinor form, a topology for Minkowski spacetime whose homeomorphism group is essentially the Lorentz group, and a careful discussion of Dirac’s famous Scissors Problem and its relation to the notion of a two-valued representation of the Lorentz group. This second edition includes a new chapter on the de Sitter universe which is intended to serve two purposes. The first is to provide a gentle prologue to the steps one must take to move beyond special relativity and adapt to the presence of gravitational fields that cannot be considered negligible. The second is to understand some of the basic features of a model of the empty universe that differs markedly from Minkowski spacetime, but may be recommended by recent astronomical observations suggesting that the expansion of our own universe is accelerating rather than slowing down. The treatment presumes only a knowledge of linear algebra in the first three chapters, a bit of real analysis in the fourth and, in two appendices, some elementary point-set topology.
The first edition of the book received the 1993 CHOICE award for Outstanding Academic Title.
Reviews of first edition:
“… a valuable contribution to the pedagogical literature which will be enjoyed by all who delight in precise mathematics andphysics.” (American Mathematical Society, 1993)
“Where many physics texts explain physical phenomena by means of mathematical models, here a rigorous and detailed mathematical development is accompanied by precise physical interpretations.” (CHOICE, 1993)
“… his talent in choosing the most significant results and ordering them within the book can’t be denied. The reading of the book is, really, a pleasure.” (Dutch Mathematical Society, 1993)
Reviews
From the reviews of the second edition:
“This text brings sophisticated mathematical structures and tools to play, yet much of the work would be accessible to a motivated undergraduate. … The author lays out his goal very clearly: ‘It is the intention of this monograph to provide an introduction to the special theory of relativity that is mathematically rigorous and yet spells out in considerable detail the physical significance of the mathematics.’ He then proceeds to accomplish this admirably. … the underlying mathematics is wonderful, worth studying for its own sake.” (William J. Satzer, The Mathematical Association of America, May, 2012)
Authors and Affiliations
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Department of Mathematics, Korman Center, Drexel University, Philadelphia, USA
Gregory L. Naber
Bibliographic Information
Book Title: The Geometry of Minkowski Spacetime
Book Subtitle: An Introduction to the Mathematics of the Special Theory of Relativity
Authors: Gregory L. Naber
Series Title: Applied Mathematical Sciences
DOI: https://doi.org/10.1007/978-1-4419-7838-7
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media, LLC 2012
Hardcover ISBN: 978-1-4419-7837-0
Softcover ISBN: 978-1-4939-0241-5
eBook ISBN: 978-1-4419-7838-7
Series ISSN: 0066-5452
Series E-ISSN: 2196-968X
Edition Number: 2
Number of Pages: XVI, 324
Topics: Manifolds and Cell Complexes (incl. Diff.Topology), Classical and Quantum Gravitation, Relativity Theory, Mathematical Methods in Physics