Communications in Mathematical Physics

, Volume 172, Issue 1, pp 187–220 | Cite as

The quantum structure of spacetime at the Planck scale and quantum fields

  • Sergio Doplicher
  • Klaus Fredenhagen
  • John E. Roberts


We propose uncertainty relations for the different coordinates of spacetime events, motivated by Heisenberg's principle and by Einstein's theory of classical gravity. A model of Quantum Spacetime is then discussed where the commutation relations exactly implement our uncertainty relations.

We outline the definition of free fields and interactions over QST and take the first steps to adapting the usual perturbation theory. The quantum nature of the underlying spacetime replaces a local interaction by a specific nonlocal effective interaction in the ordinary Minkowski space. A detailed study of interacting QFT and of the smoothing of ultraviolet divergences is deferred to a subsequent paper.

In the classical limit where the Planck length goes to zero, our Quantum Spacetime reduces to the ordinary Minkowski space times a two component space whose components are homeomorphic to the tangent bundleTS2 of the 2-sphere. The relations with Conne's theory of the standard model will be studied elsewhere.


Uncertainty Relation Classical Limit Planck Scale Minkowski Space Time Free Field 
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Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • Sergio Doplicher
    • 1
  • Klaus Fredenhagen
    • 2
  • John E. Roberts
    • 3
  1. 1.Dipartimento di MatematicaUniversità di Roma “La Sapienza”RomaItaly
  2. 2.II Institut für Theoretische Physik der Universität HamburgHamburgGermany
  3. 3.Dipartimento di MatematicaUniversità di Roma “Tor Vergata”RomaItaly

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