ミンコフスキー時空の数学 The Mathematics of Minkowski Space-Time : With an Introduction to Commutative Hypercomplex Numbers (Frontiers in Mathematics)

Boccaletti, Dino/ Catoni, F. (et al.)

Birkhäuser（2008/03発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 200 p.
• 言語 ENG
• 商品コード 9783764386139

Full Description

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.

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).