The Mathematics of Minkowski Space-Time With an Introduction to Commutative Hypercomplex Numbers
Title:
The Mathematics of Minkowski Space-Time With an Introduction to Commutative Hypercomplex Numbers
Author:
Catoni, Francesco. author.
ISBN:
9783764386146
Personal Author:
Physical Description:
XIX, 256 p. online resource.
Series:
Frontiers in Mathematics,
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).
Abstract:
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.
Added Corporate Author:
Electronic Access:
http://dx.doi.org/10.1007/978-3-7643-8614-6