2003/03/05 by Sergio Doplicher, Klaus Fredenhagen, John E. Roberts · 2 citations
Physics and Astronomy · #hep-th
paper · pdf · doi:10.1007/bf02104515
published as Commun.Math.Phys. 172 (1995) 187-220 · TeX, 37 pages. Since recent and forthcoming articles (hep-th/0105251, hep-th/0201222, hep-th/0301100) are based on this paper, we thought it would be convenient for the readers to have it available on the web
arxiv created 2003/03/05 · arxiv updated 2015/06/26
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 TS2 of the 2-sphere. The relations with Connes' theory of the standard model will be studied elsewhere.