Tullio Regge passed away a few days ago. One of the most brilliant and most creative minds of the XX century has left the world stage after a long physical decline that was cause of deep sorrow for all of his friends, colleagues, former co-workers and, of course, relatives. The influence of his ideas and the legacy of his imaginative physical-mathematical constructions will stay with us for ever. New generation scientists, sometimes not even aware of that, will develop constructions whose very conception would be unconceivable without Regge’s creations. Those who knew Tullio personally, those who interacted with him both scientifically and/or in other human and cultural activities, will never forget his very original, multi-faced and intriguing personality.
Having been one among his closest co-workers and, in some sense, his disciple, I can summarize Tullio’s deep originality and, at the same time formulate what, from my own viewpoint, is the greatest praise of his personality, by saying that he always did great things never taking them seriously. He had the curiosity and the fantasy of a child, of a very clever child, and, just as all children do, he played. His games were of very high complexity and were based on quite innovative conceptions yet, for him, they were just games, sophisticated intellectual games that attracted his attention and stimulated his creativity. The moment they appeared to be useful, the moment they unveiled their academic texture, becoming the basis for the development of a structured field of research in which many other scientists entered world-wide, that moment Tullio’s creatures completely lost the interest of their father and become to him boring. His mind turned in other directions looking for new exciting games.
What I said is best exemplified by the history of what has been one of his earliest scientific contributions, to which his family name was immediately attached, winning him a world-wide fame that led to his appointment at the Princeton Institute for Advanced Studies: I mean Regge Poles. This first achievement dates back to 1957 when Tullio, born in Torino in 1931, was only twenty-six of age. It consists of the discovery of a subtle mathematical property of potential scattering in non relativistic quantum mechanics, namely that the scattering amplitude can be thought of as an analytic function of the angular momentum which admits an extension to the complex plane, and that the positions of the poles determine power-law growth rates for the amplitude. Easily extended to the relativistic case, Regge poles opened a new era in scattering theory and provided the framework in which, ten years later, Veneziano introduced dual amplitudes and gave birth to String Theory. For more than a decade Regge poles, Regge trajectories, Regge daugthers, intercepts and the like were the common language of high energy physicists all over the world. Seminars were given, conferences were organized, both in the West and in the East, where such words were ubiquitous, yet Tullio was not taking great part in this festival, his mind being mostly concentrated on other issues. Indeed in the early 1960s, Regge introduced Regge Calculus, a simplicial formulation of General Relativity where space-time is approximated by gluing together polyhedra. Regge calculus was the first instance of discretization of a gauge theory, suitable for numerical simulation, and an early relative of lattice gauge theories. Once again Tullio’s deep originality showed up in the discovery and in the clever use of subtle analytical properties of unsuspected objects, at first sight pertaining to different provinces of physics and mathematics. The proposed object of study was gravity and the discretization of curved manifolds. The Clebsch-Gordan coefficients of the rotation group, the so named three j coefficients seemed to have nothing to do with it. Yet in the symmetries of these latter and in their analytic continuation Tullio discovered the key to solve his problem and establish his new geometrical calculus.
Very important contributions were given by him, in collaboration with Wheeler, also to the early theory of black-hole perturbations. Tullio Regge received the Dannie Heineman Prize for Mathematical Physics in 1964, the Città di Como prize in 1968, the Albert Einstein Award in 1979, and the Cecil Powell Medal in 1987. In 1996 he was awarded the Dirac Medal by the International Centre of Theoretical Physics in Trieste. Full Professor of Relativity of Torino University since 1961, he was member of the Institute of Advanced Studies in Princeton from the early sixties to 1979, when he resumed his chair in Torino. Elected to the European Parliament in 1989, when he finished his term in 1995, he was called on a special chair by the Politecnico di Torino, where he taught until his retirement. Tullio Regge was also full member of the Accademia dei Lincei and a public figure in Italy for his frequent participation to TV debates on a variety of problems ranging from Energetics to Bioethics. He was the Honorary President and co-fouder of the Società Italiana di Relatività Generale e Fisica della Gravitazione (SIGRAV).
He was also an appreciated writer of quite original popularizing books and articles. Great interest was raised by the publication of his dialogues with Primo Levi that was cured by the renown scientific journalist and writer Piero Bianucci.
Personally I am very much indebted to Tullio Regge for what he taught me during our common period of intensive scientific interaction. First of all he instilled in my mind the principle number zero to evaluate the results of one’s own calculations, i.e. the principle of beauty of numbers and of final formulae. I calculated something. If my coefficients were one, one-half, one third or may be three, Tullio said that there was a chance that I was right. If my result involved a 17 or, even worse a 23, Tullio told me that I had better to redo everything from start and he did not even want to look at my computations. Although you might learn a lot from him, he was the very antithesis of an academic professor. He had no ambition to create his own school, to educate people who would consider him their master and perpetuate his thoughts, approaches and philosophies. He was all the time a free-lancer, working for the pleasure of his own mind: he just had friends who might share his intellectual adventures or create the opportunity of new ones by posing to him their unsolved problems. He let himself be involved in any new physical or mathematical problem you would present to him. For instance his contributions to the theory of superfluidity of liquid helium and vorticity are well known and when fullerene became an object of extended study by chemical-physicists, he was fascinated by the dodecahedral symmetry group of such a molecule. Starting from there, rather then study fullerene itself, together with his collaborator of that time, namely Riccardo Zecchina, he preferred to solve a finite version of the Ising model in which the spins are located on the vertices of a platonic dodecahedron. Finite group theory helped him to solve such model to which he hilariously referred to as the soccer ball. The only condition that you had to fulfill in order to attract him to your problem is that it should be mathematically inspiring and that your motivations were purely intellectual. Starting by explaining to him the relevance of the posed issue, the far reaching consequences for Theoretical or Experimental Physics of its eventual solution, or telling him how many distinguished scientists had considered such a problem as important, was the surest way to divert his interest. He would rather show you his latest intriguing computer drawing, generated by some curious algebraic surface, or he would snow you with an unending sequence of anectodes of whose telling he was a superb and unparalled master. He had a strong sense of humour and he liked to make fun of everyone, yet always in an intelligent, friendly way that was never malicious. Addressing science as a game, the favourite targets of his jokes were all those who took themselves and the things they did seriously.
We all will miss Tullio Regge’s creativity and his ability not only to invent new conceptions, but also to stimulate the spontaneous rising of unexpected visions in the mind of his collaborators who were all the time
his affectionate friends.
Professor of Theoretical Physics, University of Torino
Scientific Counsellor of the Italian Embassy in the Russian Federation