The quantum structure of spacetime at the Planck scale and quantum fields
Abstract
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 bundle TS ^{2} of the 2sphere. The relations with Conne's theory of the standard model will be studied elsewhere.
 Publication:

Communications in Mathematical Physics
 Pub Date:
 August 1995
 DOI:
 10.1007/BF02104515
 arXiv:
 arXiv:hepth/0303037
 Bibcode:
 1995CMaPh.172..187D
 Keywords:

 High Energy Physics  Theory
 EPrint:
 TeX, 37 pages. Since recent and forthcoming articles (hepth/0105251, hepth/0201222, hepth/0301100) are based on this paper, we thought it would be convenient for the readers to have it available on the web