Gravitation in terms of observables

In the 1960s, Mandelstam proposed a new approach to gauge theories and gravity based on loops. The program was completed for Yang–Mills theories by Gambini and Trias in the 1980s. In this approach, gauge theories could be understood as representations of certain group: the group of loops. The same formalism could not be implemented at that time for the gravitational case. Here we would like to propose an extension to the case of gravity. The resulting theory is described in terms of loops and open paths and can provide the underpinning for a new quantum representation for gravity distinct from the one used in loop quantum gravity or string theory. In it, space-time points are emergent entities that would only have quasi-classical status. The formulation may be given entirely in terms of Dirac observables that form a set of gauge invariant functions that completely define the Riemannian geometry of the spacetime. At the quantum level this formulation will lead to a reduced phase space quantization free of any constraints. (paper)