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The isotropy mappings of Minkowski space-time generate the orthochronous poincaré group

Published online by Cambridge University Press:  17 February 2009

John W. Schutz
John W. Schutz
Affiliation:
Bendigo College of Advanced Eduction, Bendigo, Victoria 3550, Australia.
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Abstract

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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 Poincaré 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 Poincaré group.

Type
Research Article
Information
The ANZIAM Journal , Volume 31 , Issue 4 , April 1990 , pp. 425 - 433
Copyright
Copyright © Australian Mathematical Society 1990

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