Applied Mathematical Sciences

The Geometry of Minkowski Spacetime

An Introduction to the Mathematics of the Special Theory of Relativity

Authors: Naber, Gregory L.

  • 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
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About this Textbook

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 and physics.” (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)


Table of contents (5 chapters)

  • Introduction

    Naber, Gregory L.

    Pages 1-6

  • Geometrical Structure of M

    Naber, Gregory L.

    Pages 7-92

  • Skew-Symmetric Linear Transformations and Electromagnetic Fields

    Naber, Gregory L.

    Pages 93-133

  • The Theory of Spinors

    Naber, Gregory L.

    Pages 135-198

  • Prologue and Epilogue: The de Sitter Universe

    Naber, Gregory L.

    Pages 199-277

Buy this book

eBook $59.99
price for USA (gross)
  • ISBN 978-1-4419-7838-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $79.95
price for USA
  • ISBN 978-1-4419-7837-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $79.95
price for USA
  • ISBN 978-1-4939-0241-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
The Geometry of Minkowski Spacetime
Book Subtitle
An Introduction to the Mathematics of the Special Theory of Relativity
Authors
Series Title
Applied Mathematical Sciences
Series Volume
92
Copyright
2012
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media, LLC
eBook ISBN
978-1-4419-7838-7
DOI
10.1007/978-1-4419-7838-7
Hardcover ISBN
978-1-4419-7837-0
Softcover ISBN
978-1-4939-0241-5
Series ISSN
0066-5452
Edition Number
2
Number of Pages
XVI, 324
Topics