S. Doplicher et al., THE QUANTUM STRUCTURE OF SPACETIME AT THE PLANCK-SCALE AND QUANTUM-FIELDS, Communications in Mathematical Physics, 172(1), 1995, pp. 187-220
We propose uncertainty relations for the different coordinates of spac
etime events, motivated by Heisenberg's principle and by Einstein's th
eory of classical gravity. A model of Quantum Spacetime is then discus
sed where the commutation relations exactly implement our uncertainty
relations. We outline the definition of free fields and interactions o
ver QST and take the first steps to adapting the usual perturbation th
eory. The quantum nature of the underlying spacetime replaces a local
interaction by a specific nonlocal effective interaction in the ordina
ry Minkowski space. A detailed study of interacting QFT and of the smo
othing of ultraviolet divergences is deferred to a subsequent paper. I
n the classical limit where the Planck length goes to zero, our Quantu
m Spacetime reduces to the ordinary Minkowski space times a two compon
ent space whose components are homeomorphic to the tangent bundle TS2
of the 2-sphere. The relations with Connes' theory of the standard mod
el will be studied elsewhere.