Algebraic and geometric structures of Special Relativity

Details Algebraic and geometric structures of Special Relativity Algebraic and geometric structures of Special Relativity

2006-02-08

arxiv.org/abs/math-ph/0602018v2

Lect.Notes Phys.702:45-111,2006

Physics

Mathematical Physics

66 pages, 4 figures; v2 references added, misprints corrected

Scientific paper

10.1007/3-540-34523-X_4

I review, some of the algebraic and geometric structures that underlie the theory of Special Relativity. This includes a discussion of relativity as a symmetry principle, derivations of the Lorentz group, its composition law, its Lie algebra, comparison with the Galilei group, Einstein synchronization, the lattice of causally and chronologically complete regions in Minkowski space, rigid motion (the Noether-Herglotz theorem), and the geometry of rotating reference frames. Representation-theoretic aspects of the Lorentz group are not included. A series of appendices present some related mathematical material.

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