Kinematical Hilbert Space

This chapter covers the conceptual structure of spacetime in terms of loop states, as well as the formulation of operators which extract physical observables from these states. A toy model is introduced which illustrates how space may be subdivided into discrete units. This model motivates a dual representation of discrete space in terms of graphs with labelled edges. The model is extended and connected to Penrose’s conception of spin networks, leading to a description of spacetime as a graph labelled with spin representations. The use of these labels to define area and volume operators is then described.