Authors: Jovanović, Božidar 
Affiliations: Mechanics 
Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Affine Geometry and Relativity
Journal: Foundations of Physics
Volume: 53
First page: 60
Issue Date: 2023
Rank: ~M22
ISSN: 0015-9018
DOI: 10.1007/s10701-023-00700-2
Abstract: 
We present the basic concepts of space and time, the Galilean and pseudo-Euclidean geometry. We use an elementary geometric framework of affine spaces and groups of affine transformations to illustrate the natural relationship between classical mechanics and theory of relativity, which is quite often hidden, despite its fundamental importance. We have emphasized a passage from the group of Galilean motions to the group of Poincaré transformations of a plane. In particular, a 1-parametric family of natural deformations of the Poincaré group is described. We also visualized the underlying groups of Galilean, Euclidean, and pseudo-Euclidean rotations within the special linear group.
Keywords: Addition of velocities | Affine transformations | The Galilean and pseudo-Euclidean geometry | The Galilean principle of relativity | The Iwasawa decomposition
Publisher: Springer Link

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