Classical and Quantum Systems Foundations and Symmetries, Proceedings of the International Wigner Symposium Held in Goslar, Germany on July 16-20, 1991
Heinz Dietrich Doebner, Wolfgang Scherer, Franklin E. Schroeck
The Wigner Symposia series emerged from an International Symposium On SpaceTime Symmetries, held in College Park, Maryland, 1988 organized by Y.S. Kim and W. Zachary and commemorating the 50'th anniversary of Wigner's fundamental paper On the Unitary Representation of the Inhomogenous Lorentz Group. That symposium covered various areas of physics, of theoretical and mathematical physics to which Eugene Paul Wigner has contributed. It has shown how new and fruitful ideas connected with symmetries for a mathematical modeling of complex physical systems developed under the influence of Wigners work. Following the idea of the symposia to discuss new developments in physics centered around fundamental questions topics with emphasis on theoretical and mathematical physics were chosen and new frontiers like neuronal networks and quantum holography, whose origins can be traced back to Wigner's work, where included. The aim was to show the unity of different parts in physics and to demonstrate the power of arguments which are directly or indirectly related with mathematical realizations of symmetries. (1) Foundations of Quantum Mechanics; (2) General group Theoretical and Quantization Methods; (3) Coherent States; (4) Berry Phases; (5) Phases Space and Wigner Distributions; (6) Applications of Quantum Mechanics From Channel Space to Wigner Crystal; (7) Quantum Fields and Particles; (8) C-Algebraic and Methods; (9) Differential Geometric Methods: and (10) Nonlinear Partial Differential Equations, Dynamical Systems and Neural Networks.
The Wigner Symposia series emerged from an International Symposium On SpaceTime Symmetries, held in College Park, Maryland, 1988 organized by Y.S. Kim and W. Zachary and commemorating the 50'th anniversary of Wigner's fundamental paper On the Unitary Representation of the Inhomogenous Lorentz Group. That symposium covered various areas of physics, of theoretical and mathematical physics to which Eugene Paul Wigner has contributed. It has shown how new and fruitful ideas connected with symmetries for a mathematical modeling of complex physical systems developed under the influence of Wigners work. Following the idea of the symposia to discuss new developments in physics centered around fundamental questions topics with emphasis on theoretical and mathematical physics were chosen and new frontiers like neuronal networks and quantum holography, whose origins can be traced back to Wigner's work, where included. The aim was to show the unity of different parts in physics and to demonstrate the power of arguments which are directly or indirectly related with mathematical realizations of symmetries. (1) Foundations of Quantum Mechanics; (2) General group Theoretical and Quantization Methods; (3) Coherent States; (4) Berry Phases; (5) Phases Space and Wigner Distributions; (6) Applications of Quantum Mechanics From Channel Space to Wigner Crystal; (7) Quantum Fields and Particles; (8) C-Algebraic and Methods; (9) Differential Geometric Methods: and (10) Nonlinear Partial Differential Equations, Dynamical Systems and Neural Networks.
The Wigner Symposia deal with the most recent developments in those mathematical areas which were introduced to physics by E.P. Wigner, and also with related fields. The central themes of the proceedings of the V Wigner Symposium (WigSym5) are quantum algebra and groups, group-theoretical developments, quantum field theory and geometry, and phase space formulations of quantum mechanics. The proceedings also contain papers on the application of these techniques in various branches of physics, and contributions in which fundamental mathematical and epistemological questions related to the foundations of quantum theory are discussed.
This special issue of Journal of Physics A: Mathematical and Theoretical appears on the occasion of the 5th International Symposium on Quantum Theory and Symmetries (QTS5), held in Valladolid, Spain, from 22–28 July 2007. This is the fith in a series of conferences previously held in Goslar (Germany) 1999, QTS1; Cracow (Poland) 2001, QTS2; Cincinnati (USA) 2003, QTS3; and Varna (Bulgaria) 2005, QTS4. The QTS5 symposium gathered 181 participants from 39 countries working in different fields of theoretical physics. The spirit of the QTS conference series is to join researchers in a wide variety of topics in theoretical physics, as a way of making accessible recent results and the new lines of different fields. This is based on the feeling that it is good for a physicist to have a general overview as well as expertise in his/her own field. There are many other conferences devoted to specific topics, which are of interest to gain deeper insight in many technical aspects and that are quite suitable for discussions due to their small size. However, we believe that general conferences like this are interesting and worth keeping. We like the talks, in both plenary and parallel sessions, which are devoted to specific topics, to be prepared so as to be accessible to any researcher in any branch of theoretical physics. We think that this objective is compatible with rigour and high standards. As is well known, similar methods and techniques can be useful for many problems in different fields. We hope that this has been appreciated during the sessions of the QTS5 conference. The QTS5 conference offered the following list of topics: 1. Symmetries in string theory, quantum gravity and related topics 2. Symmetries in quantum field theories, conformal and related field theories, lattice and noncommutative theories, gauge theories 3.Quantum computing, information and control 4. Foundations of quantum theory 5. Quantum optics, coherent states, Wigner functions 6. Dynamical and integrable systems 7. Symmetries in condensed matter and statistical physics 8. Symmetries in particle physics, nuclear, atomic and molecular physics 9. Nonlinear quantum mechanics 10. Time asymmetric quantum mechanics 11. SUSY quantum mechanics, PT symmetries and pseudo-Hamiltonians 12. Mathematical methods for symmetries and quantum theories 13. Symmetries in chemistry, biology and other sciences Papers accepted for publication in this issue aim to provide a survey of the state of the art in different fields and contain contributions from plenary speakers. In addition, the issue contains contributions from other participants and it has also been open to other authors whose work fits into the topics of the conference. In any case, all the contributions have been refereed according to the high standards of Journal of Physics A: Mathematical and Theoretical . We are much indebted to several institutions; without their support the organization of the QTS5 symposium would not have been possible. In this respect we acknowledge the Ministerio de Educación of Spain and Junta de Castilla y León for general financial support; to Fundación Universidades de Castilla y León for a number of grants to young researchers who otherwise would not have attended the conference; also to the European Physical Society that provided a number of grants for eastern countries, and to the University of Valladolid where the event took place. We thank IOP Publishing and the staff of Journal of Physics A: Mathematical and Theoretical for the publication of this special issue. In addition, we want to express our gratitude to other members of the Local Organizing Committe of QTS5, who are not Editors of this special issue: Oscar Arratia, Juan A Calzada and Fernando Gómez. Finally, we would like to thank all the participants in the QTS5 conference for their presence, contributions, and for the good atmosphere achieved during their stay. We hope that the experience of spending these days in Valladolid has been most fruitful for all of them.
This Foundations of Quantum Theory special issue of Journal of Physics A: Mathematical and General contains contributions on basic aspects of modern quantum and mathematical physics. The contribution topics relate to two conferences, `Quantum Theory and Symmetries' held in Krakow (18-21 July 2001, organized by E Kapuscik and A Horzela) and `Symmetry in Sciences' held in Bregenz (23-27 July 2001, organized by B Gruber and M Ramek). Both conferences had special sessions dedicated to the memory of Professor L O'Raifeartaigh. In modern quantum physics there are several important aspects including Bell inequalities, quantum groups, nonlinear dynamics, dissipation and the time-irreversibility problem, alternative approaches and structures in quantum mechanics, quantum control, star-product quantization, etc, as well as different applications in nuclear and elementary particle physics and purely quantum effects analogous to the nonstationary Casimir effect, and different sorts of interference effects for matter waves. All of these problems were discussed at the conferences in Krakow and Bregenz and are presented in the contributions to the special issue. For example, quantum groups were found to be appropriate for the description of nonlinear dynamics and, in particular, nonlinear vibrations for which the phase of the oscillations depends on the energy. It was also found that biHamiltonian systems may correspond to different quantum pictures for the same classical equations of motion including nonlinear vibrations. Thus, it has transpired that there is an interesting link between several aspects of quantum and classical dynamics and the formalism of quantum groups. Another new quantum effect is the nonclassical behaviour of slow packets interacting with macroscopic surfaces. Quantum physics progresses rapidly and we hope that the contributions to this special issue will help readers learn more about the fundamental new aspects of quantum phenomena and the development of a mathematical formalism describing quantum and classical dynamics. Andrzej Horzela, Edward Kapuscik and Vladimir I Man'ko Guest Editors
The Wigner Centennial Conference was held in Pécs, 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.