QUANTIZATION OF THE NULL-SURFACE FORMULATION OF GENERAL-RELATIVITY

We define and discuss various quantum operators that describe the geom etry of spacetime in quantum general relativity. These are obtained by combining the null-surface formulation of general relativity, recentl y developed, with asymptotic quantization. One of the operators define d describes a ''fuzzy'' quantum light cone structure. Others, denoted ''spacetime-point operators,'' characterize geometrically defined phys ical points. We discuss the interpretation of these operators. This se ems to suggest a picture of quantum spacetime as made of ''fuzzy'' phy sical points. We derive the commutation algebra of the quantum spaceti me-point operators in the linearization around flat space.