The mathematics of Minkowski space-time : with an introduction to commutative hypercomplex numbers / Francesco Catoni ... [et al.].

Format:

Book

Contributor:

Catoni, Francesco.

Series:

Frontiers in mathematics.

Frontiers in mathematics

Language:

English

Subjects (All):

Generalized spaces.

Special relativity (Physics).

Physical Description:

1 online resource (271 p.)

Edition:

1st ed. 2008.

Place of Publication:

Basel ; Boston : Birkhauser, c2008.

Language Note:

English

Summary:

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).

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

Description based on publisher supplied metadata and other sources.

ISBN:

1-281-49123-3

9786611491239

3-7643-8614-2

OCLC:

272306915