Received: 22 June 1994 | SERGIO DOPLICHER, KLAUS FREDENHAGEN, JOHN E. ROBERTS
The paper proposes uncertainty relations for spacetime coordinates, motivated by Heisenberg's principle and Einstein's theory of classical gravity. It discusses a model of Quantum Spacetime (QST) where these uncertainty relations are implemented through commutation relations. The authors outline the definition of free fields and interactions over QST, adapting perturbation theory. They show that the quantum nature of spacetime replaces local interactions with specific nonlocal effective interactions in ordinary Minkowski space. In the classical limit, where the Planck length approaches zero, QST reduces to Minkowski space times a two-component space homeomorphic to the tangent bundle of a 2-sphere. The paper also explores spacetime uncertainties, quantum conditions on Minkowski space, and the construction of a $C^*$-algebra describing QST. The authors define spacetime integrals and develop calculus on this algebra, and provide initial steps towards quantum field theory on QST. They discuss the implications of their model for gauge theories and the classical limit, noting potential connections to Connes' theory of the standard model.The paper proposes uncertainty relations for spacetime coordinates, motivated by Heisenberg's principle and Einstein's theory of classical gravity. It discusses a model of Quantum Spacetime (QST) where these uncertainty relations are implemented through commutation relations. The authors outline the definition of free fields and interactions over QST, adapting perturbation theory. They show that the quantum nature of spacetime replaces local interactions with specific nonlocal effective interactions in ordinary Minkowski space. In the classical limit, where the Planck length approaches zero, QST reduces to Minkowski space times a two-component space homeomorphic to the tangent bundle of a 2-sphere. The paper also explores spacetime uncertainties, quantum conditions on Minkowski space, and the construction of a $C^*$-algebra describing QST. The authors define spacetime integrals and develop calculus on this algebra, and provide initial steps towards quantum field theory on QST. They discuss the implications of their model for gauge theories and the classical limit, noting potential connections to Connes' theory of the standard model.