  In the 1960's, Mandelstam proposed a new approach to gauge theories and
gravity based on loops. The program for gauge theories was completed for
Yang--Mills theories by Gambini and Trias in the 1980's. 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 complete 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.
