Preface

Abstract

This Foundations of Quantum Theory special issue of Journal of Physics A: Mathematical and Generalcontains 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.