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.

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.

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.

This is the first systematic volume which presents a detailed introduction to every facet of the modern version of Dynamical Symmetry Breaking which has been rapidly developed in recent years. Most of the lectures are given by pioneers in this new field and are geared mainly to the level of second year graduate students.

Gauge symmetries play a central role, both in the mathematical foundations as well as the conceptual construction of modern (particle) physics theories. However, it is yet unclear whether they form a necessary component of theories, or whether they can be eliminated. It is also unclear whether they are merely an auxiliary tool to simplify (and possibly localize) calculations or whether they contain independent information. Therefore their status, both in physics and philosophy of physics, remains to be fully clarified. This Element reviews the current state of affairs on both the philosophy and the physics side. In particular, it focuses on the circumstances in which the restriction of gauge theories to gauge invariant information on an observable level is warranted, using the Brout-Englert-Higgs theory as an example of particular current importance. Finally, the authors determine a set of yet to be answered questions to clarify the status of gauge symmetries.

This volume includes discussion on new dynamical features in the light of (deconstruted/latticized) extra dimensions, holographic QCD, Moose/hidden local symmetry, and so on. New insights into the QCD as a prototype of strong coupling gauge theories as well as in its own right, particularly in hot and dense matter are included.

This volume includes discussion on new dynamical features in the light of (deconstruted/latticized) extra dimensions, holographic QCD, Moose/hidden local symmetry, and so on. New insights into the QCD as a prototype of strong coupling gauge theories as well as in its own right, particularly in hot and dense matter are included.

Topological defects formed at symmetry-breaking phase transitions play an important role in many different fields of physics. They appear in many condensed-matter systems at low temperature; examples include vortices in superfluid helium-4, a rich variety of defects in helium-3, quantized mag netic flux tubes in type-II superconductors, and disclination lines and other defects in liquid crystals. In cosmology, unified gauge theories of particle interactions suggest a sequence of phase transitions in the very early uni verse some of which may lead to defect formation. In astrophysics, defects play an important role in the dynamics of neutron stars. In 1997 the European Science Foundation started the scientific network "Topological defects" headed by Tom Kibble. This network has provided us with a unique opportunity of establishing a collaboration between the representatives of these very different branches of modern physics. The NATO-ASI (Advanced Study Institute), held in Les Houches in February 1999 thanks to the support of the Scientific Division of NATO, the European Science Foundation and the CNRS, represents a key event of this ESF network. It brought together participants from widely different fields, with diverse expertise and vocabulary, fostering the exchange of ideas. The lectures given by particle physicists, cosmologists and condensed matter physicists are the result of the fruitful collaborations established since 1997 between groups in several European countries and in the U.S.A.

What Is Time Crystal In condensed matter physics, a time crystal is a quantum system of particles whose lowest-energy state is one in which the particles are in repetitive motion. The system cannot lose energy to the environment and come to rest because it is already in its quantum ground state. Because of this the motion of the particles does not really represent kinetic energy like other motion, it has "motion without energy". Time crystals were first proposed theoretically by Frank Wilczek in 2012 as a time-based analogue to common crystals whereas the atoms in crystals are arranged periodically in space, the atoms in a time crystal are arranged periodically in both space and time. Several different groups have demonstrated matter with stable periodic evolution in systems that are periodically driven. In terms of practical use, time crystals may one day be used as quantum memories. How You Will Benefit (I) Insights, and validations about the following topics: Chapter 1: Time crystal Chapter 2: Time translation symmetry Chapter 3: Crystal structure Chapter 4: Spontaneous symmetry breaking Chapter 5: Condensed matter physics Chapter 6: Quantum mechanics Chapter 7: Zero-point energy (II) Answering the public top questions about time crystal. (III) Real world examples for the usage of time crystal in many fields. (IV) 17 appendices to explain, briefly, 266 emerging technologies in each industry to have 360-degree full understanding of time crystal' technologies. Who This Book Is For Professionals, undergraduate and graduate students, enthusiasts, hobbyists, and those who want to go beyond basic knowledge or information for any kind of time crystal.