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Physics Today

The mathematics of quantum theory

G. Luzzatto, Arthur S. Wightman

Published Sep 1, 1959• 0 citations
Publisher

Abstract

From July 21 to August 9, 1958, a summer course on Mathematical Problems of Quantum Theory of Particles and Fields was held in Varenna, Italy. The lectures took place in the Villa Monastero, on the shores of beautiful Lake Como; the place is well known to the readers of Physics Today since in other issues (Dec. 1957, Jan. 1958) there have been reports about conferences held there, and about other courses of the International School of Physics. The school is organized by the Italian Physical Society and is sponsored by the Italian National Science Council, by the Italian Government, by some Italian universities, by various local representatives, and occasionally by other institutions. Each summer it gives a number of courses (recently three or four), on special topics in physics. These courses are neither meetings of experts, nor quick courses at the graduate-school level. The goal is to put the persons with most experience in a field in touch with the younger or less experienced, in order to give the latter an up-to-date picture of recent research and open problems. The courses are organized quite independently and vary in length from a few days to three weeks in the present case.

DOI
10.1063/1.3060963

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From July 21 to August 9, 1958, a summer course on Mathematical Problems of Quantum Theory of Particles and Fields was held in Varenna, Italy. The lectures took place in the Villa Monastero, on the shores of beautiful Lake Como; the place is well known to the readers of Physics Today since in other issues (Dec. 1957, Jan. 1958) there have been reports about conferences held there, and about other courses of the International School of Physics. The school is organized by the Italian Physical Society and is sponsored by the Italian National Science Council, by the Italian Government, by some Italian universities, by various local representatives, and occasionally by other institutions. Each summer it gives a number of courses (recently three or four), on special topics in physics. These courses are neither meetings of experts, nor quick courses at the graduate-school level. The goal is to put the persons with most experience in a field in touch with the younger or less experienced, in order to give the latter an up-to-date picture of recent research and open problems. The courses are organized quite independently and vary in length from a few days to three weeks in the present case.
This Fermi Summer School of Physics on Experimental Quantum Information and Computing represents a primer in an expanding area in physics. In this part, the interest in quantum information (QI) science is due to the discovery that a computer operating on quantum mechanical principles can solve certain important computational problems exponentially faster than any conceivable classical computer. But this interest is also due to the interdisciplinary nature of the field: the rapid growth is attributable, in part, to the stimulating confluence of researchers and ideas from physics, chemistry, mathematics, information theory, and computer science. The lectures cover Quantum Information (QI) processing, spanning quantum optics and laser physics, atomic and molecular physics, physical chemistry, and condensed-matter physics.
This book is the first volume of the proceedings of the Canadian Mathematical Society Annual Seminar on Mathematical Quantum Theory, held in Vancouver in August 1993. The seminar was run as a research-level summer school concentrating on two related areas of contemporary mathematical physics. The subject of the first session, quantum field theory and many-body theory, is covered in the present volume; papers from the second session, on Schr odinger operators, are in Volume 2. Each session featured a series of minicourses, consisting of approximately four one-hour lectures, designed to introduce students to current research in a particular area. In addition, about thirty speakers gave one-hour expository lectures. With contributions by some of the top experts in the field, this book provides an overview of the state of the art in mathematical quantum field and many-body theory.
The fourth International Workshop on `Mysteries, Puzzles and Paradoxes in Quantum Mechanics' was held from 27 August to 1 September 2001, at the Palazzo Feltrinelli in Gargnano, Italy, as were the first three, on the shore of Lake Garda. It continued the tradition of the previous workshops in seeking a deeper understanding of the foundations of quantum mechanics. After more than 75 years, this field of investigation is still active and able to stimulate both intense discussions and interesting physics research, involving many physicists from quite different fields. For that reason, this special issue of Journal of Optics B: Quantum and Semiclassical Optics confronts many different aspects of quantum mechanics, as afforded from many different points of view. There is, however, a common theme pervading all the contributions, which provided the main focus of this workshop, namely, interference. We have followed Richard Feynman, according to whom quantum interference is a `phenomenon which is impossible, absolutely impossible, to explain in any classical way, and which has in it the heart of quantum mechanics. In reality it contains the only mystery.' The workshop investigated many aspects of interference phenomena in various fields of optical, atomic and molecular physics. The progressive degradation of interference effects, i.e. quantum decoherence, was also investigated in its various forms, both experimentally and theoretically. In fact, this special issue demonstrates another distinguishing feature of the series of `Mysteries, Puzzles and Paradoxes in Quantum Mechanics', namely, the close connection between theoretical and experimental contributions. This strong interconnection is becoming more and more important nowadays, because of the impressive technological advances which have made it possible to verify experimentally in a laboratory what the founding fathers of quantum mechanics considered only as `Gedanken' experiments. The intense debate and lively atmosphere of the workshop is reflected by the 44 contributions to this special issue, involving more than 90 authors. We would like to give special thanks to Giovanna La Pietra, the real cornerstone of all four of the workshops; without her continuous assistance, they would have not been possible. Finally, special thanks are due to the Scientific Secretary of the workshop, Dr Stefano Olivares, for his invaluable help, both in organizing the meeting and in the preparation of this special issue. Rodolfo Bonifacio Università di Milano, Italy David Vitali Università di Camerino, Italy Guest Editors