Dynamical Symmetry

Whenever systems are governed by continuous chains of causes and effects, their behavior exhibits the consequences of dynamical symmetries, many of them far from obvious. Dynamical Symmetry introduces the reader to Sophus Lie's discoveries of the connections between differential equations and continuous groups that underlie this observation. It develops and applies the mathematical relations between dynamics and geometry that result. Systematic methods for uncovering dynamical symmetries are described, and put to use. Much material in the book is new and some has only recently appeared in research journals. Though Lie groups play a key role in elementary particle physics, their connection with differential equations is more often exploited in applied mathematics and engineering. Dynamical Symmetry bridges this gap in a novel manner designed to help readers establish new connections in their own areas of interest. Emphasis is placed on applications to physics and chemistry. Applications to many of the other sciences illustrate both general principles and the ubiquitousness of dynamical symmetries.

The phenomenon of dynamical symmetry breaking (DSB) in quantum field theory is discussed in a detailed and comprehensive way. The deep connection between this phenomenon in condensed matter physics and particle physics is emphasized. The realizations of DSB in such realistic theories as quantum chromodynamics and electroweak theory are considered. Issues intimately connected with DSB such as critical phenomenona and effective lagrangian approach are also discussed.

Group theoretical concepts elucidate fundamental physical phenomena, including excitation spectra of quantum systems and complex geometrical structures such as molecules and crystals. These concepts are extensively covered in numerous textbooks. The aim of the present monograph is to illuminate more subtle aspects featuring group theory for quantum mechanics, that is, the concept of dynamical symmetry. Dynamical symmetry groups complement the conventional groups: their elements induce transitions between states belonging to different representations of the symmetry group of the Hamiltonian. Dynamical symmetry appears as a hidden symmetry in the hydrogen atom and quantum rotator problem, but its main role is manifested in nano and meso systems. Such systems include atomic clusters, large molecules, quantum dots attached to metallic electrodes, etc. They are expected to be the building blocks of future quantum electronic devices and information transmitting algorithms. Elucidation of the electronic properties of such systems is greatly facilitated by applying concepts of dynamical group theory.

The Highly Specialized Seminar on "Symmetries in Nuclear Structure", held in Erice, Italy, in March 2003, celebrated the career and the remarkable achievements of Francesco Iachello, on the occasion of his 60th birthday. Since the development of the interacting boson model in the early 1970s, the ideas of Iachello have provided a variety of frameworks for understanding collective behaviour in nuclear structure, founded on the concepts of dynamical symmetries and spectrum-generating algebras. The original ideas, which were developed for the description of atomic nuclei, have now been successfully extended to cover spectroscopic behaviour in other fields, such as molecular or hadronic spectra. More recently, the suggestion by Iachello of critical point symmetries to treat nuclei in shape/phase transitional regions has opened an exciting new front for both theoreticians and experimentalists.The talks presented at the meeting covered many of the most active forefront areas of nuclear structure as well as other fields where ideas of symmetries are being explored. Topics in nuclear structure included extensive discussions on dynamical symmetries, critical point symmetries, phase transitions, statistical properties of nuclei, supersymmetry, mixed symmetry states, shears bands, pairing and clustering in nuclei, shape coexistence, exotic nuclei, dipole modes, and astrophysics, among others. In addition, important sessions focused on talks by European laboratory directors (or their representatives) outlining prospects for nuclear structure, and the application of symmetry ideas to molecular phenomena. Finally, a special lecture by Nobel laureate Alex Mueller, on s and d wave symmetry in superconductors, presented a unique insight into an allied field.The proceedings have been selected for coverage in:* Index to Scientific & Technical Proceedings� (ISTP� / ISI Proceedings)* Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings)* CC Proceedings -- Engineering & Physical Sciences

The phenomenon of dynamical symmetry breaking (DSB) in quantum field theory is discussed in a detailed and comprehensive way. The deep connection between this phenomenon in condensed matter physics and particle physics is emphasized. The realizations of DSB in such realistic theories as quantum chromodynamics and electroweak theory are considered. Issues intimately connected with DSB such as critical phenomenona and effective lagrangian approach are also discussed.

Describes methods revealing the structures and dynamics of turbulence for engineering, physical science and mathematics researchers working in fluid dynamics.

This book is a collection of original papers on dynamical gauge symmetry breaking, and is intended for graduate students and researchers in theoretical physics (elementary particle physics and others) who have an understanding of basic quantum field theory. The book can serve as a research text for those requiring an introduction to dynamical gauge symmetry breaking and as a reference text for active researchers. The important papers in the field that are included deal with attempts to apply the ideas to realistic models of elementary particle interactions. A historical critique by the editors provides an introductory review.