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

By: Catoni, Francesco [author.].
Contributor(s): Boccaletti, Dino [author.1] | Cannata, Roberto [author.1] | Catoni, Vincenzo [author.1] | Nichelatti, Enrico [author.1] | Zampetti, Paolo [author.2] | SpringerLink (Online service)0.
Material type: materialTypeLabelBookSeries: Frontiers in Mathematics.Publisher: Basel : Birkh�user Basel, 2008. Description: XIX, 256 p. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783764386146.Subject(s): Mathematics | Topological groups | Lie groups | Mathematical analysis | Analysis (Mathematics) | Geometry | Differential geometry | Physics.1 | Mathematics.2 | Geometry.2 | Differential Geometry.2 | Mathematical Methods in Physics.2 | Topological Groups, Lie Groups.2 | Analysis.1DDC classification: 516 Online resources: Click here to access online
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).
In: Springer eBooks0Summary: 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.
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Item type Current location Call number Status Date due Barcode Item holds
PK Kelkar Library, IIT Kanpur
Available EBK10447
Total holds: 0

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).

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.

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