The Mathematics of Minkowski Space-Time
Springer Basel (Verlag)
978-3-7643-8613-9 (ISBN)
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.
N-Dimensional Commutative Hypercomplex Numbers.- The Geometries Generated by Hypercomplex Numbers.- Trigonometry in the Minkowski Plane.- Uniform and Accelerated Motions in the Minkowski Space-Time (Twin Paradox).- General Two-Dimensional Hypercomplex Numbers.- Functions of a Hyperbolic Variable.- Hyperbolic Variables on Lorentz Surfaces.- Constant Curvature Lorentz Surfaces.- Generalization of Two-Dimensional Special Relativity (Hyperbolic Transformations and the Equivalence Principle).
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)
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)
| Erscheint lt. Verlag | 17.4.2008 |
|---|---|
| Reihe/Serie | Frontiers in Mathematics |
| Zusatzinfo | XIX, 256 p. |
| Verlagsort | Basel |
| Sprache | englisch |
| Maße | 170 x 244 mm |
| Gewicht | 550 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Geometrie / Topologie |
| Schlagworte | Differentialgeometrie • Differenzialgeometrie • gauss differential geometry • Hardcover, Softcover / Mathematik/Geometrie • HC/Mathematik/Geometrie • hyperbolic numbers • hypercomplex numbers • Lorentz surfaces • Matrix • Minkowski space • Minkowski space-time • Minkowski-Welt • Special relativity • twin paradox |
| ISBN-10 | 3-7643-8613-4 / 3764386134 |
| ISBN-13 | 978-3-7643-8613-9 / 9783764386139 |
| Zustand | Neuware |
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