Wigner Centennial issue

Abstract

The Wigner Centennial Conference was held in Pecs, Hungary, on 8–12 July 2002. Eugene Paul Wigner was born in Budapest on 17 November 1902 and left us on 1 January 1995 in Princeton, USA. Numerous other conferences and conference sessions were also held during 2002 to commemorate the centennial year of his birth, because so many wished to pay tribute to him. It would, of course, take a major international effort to review thoroughly all the contributions Wigner made in all branches of physics and for the cause of world peace. The purpose of the Wigner Centennial Conference was to enrich and enhance the research lines initiated by Wigner. The conference was particularly interested in assembling young researchers who will develop and expand those research lines in the future. Indeed, there were many papers of current interest, including symmetry problems in quantum mechanics and quantum field theory, group theoretical issues, foundations of quantum mechanics, nuclear physics, chemical physics, the phase-space formulation of quantum mechanics, as well as quantum computing, information and entanglement problems. In 1932 Wigner published a seminal paper entitled 'On the quantum correction for thermodynamic equations' (Phys. Rev. 40 749--759) in which he introduced a fundamental tool for quantum mechanics known these days as the Wigner function. The Wigner function has a long history, but began to gain its major strength in quantum optics during the 1970s. Since then, it has become the primary scientific language for squeezed states of light dealing with multi-photon coherent states. The Wigner function is also the basic language for transition from classical to quantum mechanics through phase-space. It therefore plays a major role in detecting quantum effects in processes routinely regarded as classical. Indeed, most optical instruments have been based on classical optics; it is, however, a great challenge to find quantum effects in those devices. This itself is an important subject. Wigner initially formulated the Wigner function to understand thermodynamic effects in physical systems, and thus it plays an important role in studying entropy in measurement processes, statistical mechanics and chemical physics. Physicists do not seem to fully appreciate the fact that Wigner functions can be used for the purpose of group representations. For instance, the single-mode and two-mode squeezed states are isomorphic to the Lorentz groups O(2,1) and O(3,2), respectively. This can be done very cleanly within the framework of the Wigner phase-space approach. By combining two of Wigner's main research areas, namely group theory and the Wigner function, we can construct a very rich field of physics. This is a future possibility for today's young physicists. Turning to computing, a man or woman is born with ten fingers, which constitute a natural computer based on decimal numbers. Indeed, the Chinese developed an abacus for dealing with decimal numbers. Slide rules perform additions, but they can do multiplications in the logarithmic scale. In the 1940s, another Hungarian scientist named John von Neumann observed that vacuum tubes could perform 'yes or no' logic. His observation led to the computer age in which we live. It is interesting to note that both Wigner and von Neumann came from the same high school in Hungary, the Budapest Evangelikus Gimnazium. Likewise, Eugene Wigner began to worry about the language that atoms speak even before the present form of quantum mechanics was formulated. He published in 1929 a book entitled 'Group Theory and its Applications to Quantum Mechanics of Atomic Spectra'. This is, in fact, the first book on quantum computing. Physicists do not yet seem to appreciate this aspect of Wigner's contribution, but eventually they will. If we are seriously interested in building quantum computers, we should use atoms. We should then develop mathematical algorithms to use group theory of atomic spectra for numerical computation. This is what Wigner left to us as a homework. The Wigner Centennial Conference was dedicated to Wigner's future rather than to his past. Indeed, we are very happy to note that many young physicists presented their new research results at this conference. We regret that this special issue cannot include all the subjects covered at the Conference. We are, however, very fortunate to have so many excellent papers on Wigner functions, quantum optics and quantum information, as well as quantum computing. The special issue is not meant to be the conference proceedings. The papers included here have been refereed according to the standards of Journal of Optics B: Quantum and Semiclassical Optics and publication was not restricted to the participants of the Conference. This is indeed a special issue dedicated to the above-mentioned subjects.