Chapter 9: Conclusions

We have reviewed how the application of new techniques, based on the field lines that originated with Faraday long time ago and applied to gravity rewritten as Abhay Ashtekar taught us, has allowed to build a quantum theory of gravity. We still do not have complete control over it, but it has been applied to a couple of interesting situations and has yielded attractive results. There is much left to be done. But we hope the reader can appreciate that this mixture of the Faraday lines, the spin networks of Penrose, and the notion of diffeomorphism invariance have led to new insights on the problem of quantum gravity…