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The Mathematics of Minkowski Space-Time

With an Introduction to Commutative Hypercomplex Numbers

  • Book
  • © 2008

Overview

Authors:
  1. Francesco Catoni

    1. Roma, Italy

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  2. Dino Boccaletti

    1. Dipartimento di Matematica, Università di Roma “La Sapienza”, Roma, Italy

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  3. Roberto Cannata

    1. C.R. Casaccia, ENEA, Roma, Italy

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  4. Vincenzo Catoni

    1. Roma, Italy

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  5. Enrico Nichelatti

    1. C.R. Casaccia, ENEA, Roma, Italy

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  6. Paolo Zampetti

    1. C.R. Casaccia, ENEA, Roma, Italy

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Part of the book series: Frontiers in Mathematics (FM)

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-xix
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  2. Introduction

    Pages 1-3

  3. N-Dimensional Commutative Hypercomplex Numbers

    Pages 5-17

  4. The Geometries Generated by Hypercomplex Numbers

    Pages 19-25

  5. Trigonometry in the Minkowski Plane

    Pages 27-56

  6. Uniform and Accelerated Motions in the Minkowski Space-Time (Twin Paradox)

    Pages 57-72

  7. General Two-Dimensional Hypercomplex Numbers

    Pages 73-86

  8. Functions of a Hyperbolic Variable

    Pages 87-117

  9. Hyperbolic Variables on Lorentz Surfaces

    Pages 119-135

  10. Constant Curvature Lorentz Surfaces

    Pages 137-160

  11. Generalization of Two-Dimensional Special Relativity (Hyperbolic Transformations and the Equivalence Principle)

    Pages 161-168

  12. Back Matter

    Pages 169-255
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Keywords

About this book

Hyperbolic numbers are proposed for a rigorous geometric formalization of the space-time symmetry of two-dimensional Special Relativity. The system of hyperbolic numbers as a simple extension of the field of complex numbers is extensively studied in the book. In particular, an exhaustive solution of the "twin paradox" is given, followed by a detailed exposition of space-time geometry and trigonometry. Finally, an appendix on general properties of commutative hypercomplex systems with four unities is presented.

Reviews

From the reviews: “It is worth pointing out that the book is mainly a text about commutative hypercomplex numbers and some of their applications to a 2-dimensional Minkowski spacetime. … This book should be interesting to anybody who is interested in applications of hypercomplex numbers … . In conclusion, I recommend this book to anyone who wants to learn about hypercomplex numbers.” (Emanuel Gallo, Mathematical Reviews, Issue 2010 d)

Authors and Affiliations

  • Roma, Italy

    Francesco Catoni, Vincenzo Catoni

  • Dipartimento di Matematica, Università di Roma “La Sapienza”, Roma, Italy

    Dino Boccaletti

  • C.R. Casaccia, ENEA, Roma, Italy

    Roberto Cannata, Enrico Nichelatti, Paolo Zampetti

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