Communications in Mathematical Physics

, Volume 28, Issue 3, pp 259–266 | Cite as

The structure of space-time transformations

  • H. J. Borchers
  • G. C. Hegerfeldt


LetT be a one-to-one mapping ofn-dimensional space-timeM onto itself. IfT maps light cones onto light cones and dimM≧3, it is shown thatT is, up to a scale factor, an inhomogeneous Lorentz transformation. Thus constancy of light velocity alone implies the Lorentz group (up to dilatations). The same holds ifT andT−1 preserve (xy)2>0. This generalizes Zeeman's Theorem. It is then shown that ifT maps lightlike lines onto (arbitrary) straight lines and if dimM≧3, thenT is linear. The last result can be applied to transformations connecting different reference frames in a relativistic or non-relativistic theory.


Neural Network Statistical Physic Complex System Reference Frame Nonlinear Dynamics 
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Copyright information

© Springer-Verlag 1972

Authors and Affiliations

  • H. J. Borchers
    • 1
  • G. C. Hegerfeldt
    • 1
  1. 1.Institut für Theoretische PhysikUniversität GöttingenGöttingenGermany

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