The Mathematics of Minkowski Space-Time With an Introduction to Commutative Hypercomplex Numbers /

• Main Authors: Catoni, Francesco (Author), Boccaletti, Dino (Author), Cannata, Roberto (Author), Catoni, Vincenzo (Author), Nichelatti, Enrico (Author), Zampetti, Paolo (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Basel : Birkhäuser Basel, 2008.
• Series: Frontiers in Mathematics,
• Subjects: Mathematics.; Topological groups.; Lie groups.; Mathematical analysis.; Analysis (Mathematics).; Geometry.; Differential geometry.; Physics.; Differential Geometry.; Mathematical Methods in Physics.; Topological Groups, Lie Groups.; Analysis.

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...

Table of Contents:

• 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).