J Austral Math Soc Ser B 31 pp425--433, 1990.

The isotropy mappings of Minowski space-time generate the orthochronous Poincare group

John W. Schutz

(Received 17 November 1988; revised 22 June 1989)

Abstract

Minkowski space-time is specified with respect to a single coordinate frame by the set of timelike lines. Isotropy mappings are defined as automorphisms which leave the events of one timelike line invariant. We demonstrate the existence of two special types of isotropy mappings. The first type of isotropy mapping induce orthogonal transformations in position space. Mappings of the second type can be composed to generate Lorentz boosts. It is shown that isotropy mappings generate the orthochronous Poincarë group of motions. The set of isotropy mappings then maps the single assumed coordinate frame onto a set of coordinate frames related by transformations of the orthochronous Poincarë group.

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Author

John W. Schutz: Bendigo College of Advanced Education, Bendigo, Victoria 3550, Australia.

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Last Modified: Mon Jan 14 16:50:21 2002