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Zur Kennzeichnung der Lorentz-Transformationen

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Abstract

Let (V, f) be a real Minkowski space of any, not necessarily finite, dimension, and letd be the corresponding distance function (taking negative values for timelike distances). Then the following statement (among others) is proved: If ϕ :V →V is a surjective mapping such that

$$d(P,Q) = a \Leftrightarrow d(P^\varphi ,Q^\varphi ) = a\forall P,Q \in V$$

is true for some fixeda εR,a<0, then ϕ is a Lorentz transformation (including a possible translation).

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Literatur

  1. Alexandrov, A. D. andOvchinnikova, V. V.,Notes on the foundations of relativity theory. Vestnik Leningrad. Univ.,11 (1953), 95.

    Google Scholar 

  2. Alexandrov, A. D.,The space-time of the theory of relativity. Jubilee of Relativity Theory, Proceedings, Basel, 1956.

  3. Alexandrov, A. D.,A contribution to cronogeometry, Canad. J. Math.19 (1967), 1119–1128.

    Google Scholar 

  4. Beckman, F. S. andQuarles, D. A. Jr.,On isometries of Euclidean spaces. Proc. Amer. Math. Soc.4 (1953), 810–815.

    Google Scholar 

  5. Benz, W.,Zur Charakterisierung der Lorentz-Transformationen. Wird veröffentlicht.

  6. Benz, W.,A Characterization of Plane Lorentz Transformations. Wird veröffentlicht.

  7. Borchers, H. J. andHegerfeld, G. C.,The structure of space-time transformations. Commun. Math. Phys.28 (1972), 259–266.

    Google Scholar 

  8. Farrahi, B.,On Isometries of Euclidean Planes. J. Geometry6 (1975), 89–92.

    Google Scholar 

  9. Suppes, P.,Axioms for relativistic kinematics with or without parity. In "The axiomatic method", Henkin, L. et al eds., North Holland, Amsterdam, 1959, 291–307.

    Google Scholar 

  10. Vogt, A.,On the Linearity of Form Isometries. Siam J. Appl. Math.22 (1972), 553–560.

    Google Scholar 

  11. Zeeman, E. C.,Causality implies the Lorentz group, J. Mathematical Phys.5 (1964), 490–493.

    Google Scholar 

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Authors and Affiliations

  1. Mathematisches Seminar der Universität, Bundesstr. 55, 2 Hamburg 13, Germany

    Eberhard M. Schröder

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  1. Eberhard M. Schröder
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Schröder, E.M. Zur Kennzeichnung der Lorentz-Transformationen. Aeq. Math. 19, 134–144 (1979). https://doi.org/10.1007/BF02189861

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  • DOI: https://doi.org/10.1007/BF02189861

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