THE QUANTUM STRUCTURE OF SPACETIME AT THE PLANCK-SCALE AND QUANTUM-FIELDS

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.