Abstract
We define and discuss various quantum operators that describe the geometry of spacetime in quantum general relativity. These are obtained by combining the null-surface formulation of general relativity, recently developed, with asymptotic quantization. One of the operators defined describes a “fuzzy” quantum light cone structure. Others, denoted “spacetime-point operators,” characterize geometrically defined physical points. We discuss the interpretation of these operators. This seems to suggest a picture of quantum spacetime as made of “fuzzy” physical points. We derive the commutation algebra of the quantum spacetime-point operators in the linearization around flat space.
- Received 17 October 1996
DOI:https://doi.org/10.1103/PhysRevD.56.889
©1997 American Physical Society