It is customary for me, during my holidays, to read some technical books that I bear with me at Satriano, a small town very near Soverato. This summer I have read the book of Stephan Narison on QCD as QCD is currently my work and this is a really beautiful book. But I have written papers on almost all fields of physics and in the summer of 2005 I was struggling with general relativity. That year I took with me a wonderful book by James Hartle: “Gravity: An Introduction to Einstein’s General Relativity” . This book has been a source of inspiration for my work. Indeed, in a few days I was trying to apply my well developed approach for strong perturbations to Schwarzschild solution. This was a blind alley as I was manipulating an exact solution that has no much to say for perturbation techniques. As I looked at the problem more in depth, I was able to make this application to general relativity in a paper published on International Journal of Modern Physics D (see here for a preprint). I have to thank the editor Jorge Pullin for appreciating my work. I met him in Piombino at DICE 2006 Conference where he gave a very nice talk.
This paper has been a fundamental starting point for all my succesive work for two main reasons: Firstly, I have understood that to solve strongly perturbed partial differential equations one has to recur to a gradient expansion and secondly, this paper gives a sensible proof of the Belinski-Khalatnikov-Lifshitz (BKL) conjecture that permits to understand why near a singularity the space-time is homogeneous. Vladimir Belinski has been a professor of mine at University “La Sapienza” of Rome in 1992. He taught me general relativity with the more exotic solutions: BKL and gravisolitons. He is also well-known for having written down parts of Landau-Lifshitz book about this matter. I remember a nice talk with him in those days about BKL and for this reason I acknowledged him in my paper. Indeed, after speaking with him I should have been able to catch immediately the answer but times were not so mature and I have had to do a lot of work and thinking before to arrive at this successful point.
After understanding how to do strong perturbation theory to partial differential equations, my next step was to find a way to generalize it to quantum field theory. In a few days I was able to do it and this became a paper for Physical Review D (see here for a preprint). In this paper I improve on the Bender’s approach (see here) obtaining the propagator and the spectrum for a massless scalar theory showing that in the infrared this theory acquires a mass gap. A real successful improvement!
After that stunning summer, I have been able to extend all this to Yang-Mills and QCD but we are talking about today…