there seemed to be insurmountable mathematical difficulties in promoting the constraints to quantum operators because of their highly non-linear dependence on the canonical variables. The equations were much simplified with the introduction of Ashtekars new variables. Ashtekar variables describe canonical general relativity in terms of a new pair canonical variables closer to that of gauge theories. In doing so it introduced an additional constraint, on top of the spatial diffeomorphism and Hamiltonian constraint, the Gauss gauge constraint. The loop representation is a quantum hamiltonian representation of gauge theories in terms of loops. The aim of the loop representation, in the context of Yang–Mills theories is to avoid the redundancy introduced by Gauss gauge symmetries allowing to work directly in the space of Gauss gauge invariant states. The use of this representation arose naturally from the Ashtekar–Barbero representation as it provides an exact non-perturbative description and also because the spatial diffeomorphism constraint is easily dealt with within this representation. Within the loop representation Thiemann has provided a well defined canonical theory in the presence of all forms of matter and explicitly demonstrated it to be manifestly finite! So there is no need for renormalization. However, as LQG approach is well suited to describe physics at the Planck scale, there are difficulties in making contact with familiar low energy physics and establishing it has the correct semi-classical limit. The problem of time All canonical theories of general relativity have to deal with the problem of time. In quantum gravity, the problem of time is a conceptual conflict between general relativity and quantum mechanics. In canonical general relativity, time is just another coordinate as a result of general covariance. In quantum field theories, especially in the Hamiltonian formulation, the formulation is split between three dimensions of space, and one dimension of time. Roughly speaking, the problem of time is that there is none in general relativity. This is because in general relativity the Hamiltonian is a constraint that must vanish. However, in any canonical theory, the Hamiltonian generates time translations. Therefore, we arrive at the conclusion that "nothing moves" ("there is no time") in general relativity. Since "there is no time", the usual interpretation of quantum mechanics measurements at given moments of time breaks down. This problem of time is the broad banner for all interpretational problems of the formalism. A canonical formalism of James York's conformal decomposition of geometrodynamics, leading to the