Catoni / Boccaletti / Cannata The Mathematics of Minkowski Space-Time

With an Introduction to Commutative Hypercomplex Numbers
1. Auflage 2008
ISBN: 978-3-7643-8614-6
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 256 Seiten, Web PDF

Reihe: Mathematics and Statistics

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.

Zielgruppe

Research

Autoren/Hrsg.

Catoni, Francesco

Boccaletti, Dino

Cannata, Roberto

Catoni, Vincenzo

Nichelatti, Enrico

Zampetti, Paolo

Inhaltsverzeichnis

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).