The new edition of this well received primer on rigorous aspects of symmetry breaking presents a more detailed and thorough discussion of the mechanism of symmetry breaking in classical field theory in relation with the Noether theorem. Moreover, the link between symmetry breaking without massless Goldstone bosons in Coulomb systems and in gauge theories is made more explicit. A subject index has been added and a number of misprints have been corrected.
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.
The book provides a non-perturbative approach to the symmetry breaking in the standard model, in this way avoiding the critical issues which affect the standard presentations. The debated empirical meaning of global and local gauge symmetries is clarified. The absence of Goldstone bosons in the Higgs mechanism is non-perturbatively explained by the validity of Gauss laws obeyed by the currents which generate the relatedglobal gauge symmetry. The solution of the U(1) problem and the vacuum structure in quantum chromodynamics (QCD) are obtained without recourse to the problematic semiclassical instanton approximation, by rather exploiting the topology of the gauge group.
This book discusses group theory investigations of zincblende and wurtzite semiconductors under symmetry-breaking conditions. The text presents the group theory elements required to develop a multitude of symmetry-breaking problems, giving scientists a fast track to bypass the need for recalculating electronic states. The text is not only a valuable resource for speeding up calculations but also illustrates the construction of effective Hamiltonians for a chosen set of electronic states in crystalline semiconductors. Since Hamiltonians have to be invariant under the transformations of the point group, the crystal symmetry determines the multiplet structure of these states in the presence of spin-orbit, crystal-field, or exchange interactions. Symmetry-breaking leads to additional coupling of the states, resulting in shifts and/or splittings of the multiplets. Such interactions may be intrinsic, as in the case of the quasi-particle dispersion, or extrinsic, induced by magnetic, electric, or strain fields. Using a power expansion of the perturbations these interaction terms can be determined in their parameterized form in a unique way. The hierarchic structure of this invariant development allows to estimate the importance of particular symmetry-breaking effects in the Hamiltonian. A number of selected experimental curves are included to illustrate the symmetry-based discussions, which are especially important in optical spectroscopy. This text is written for graduate students and researchers who want to understand and simulate experimental findings reflecting the fine structure of electronic or excitonic states in crystalline semiconductors.
Experts examine the mechanisms by which cells polarize, divide asymmetrically, and produce asymmetric structures, providing examples from bacteria, yeast, plants, invertebrates, and mammals. Discussion include the molecular basis of polarization, mechanisms, and more.
Learn quantum field theory relatively easily Trying to comprehend quantum field theory but don't have infinite time or the IQ of Einstein? No problem! This easy-to-follow guide helps you understand this complex subject matter without spending a lot of energy. Quantum Field Theory Demystified covers essential principles such as particle physics and special relativity. You'll learn about Lagrangian field theory, group theory, and electroweak theory. The book also explains continuous and discrete symmetries, spontaneous symmetry breaking, and supersymmetry. With thorough coverage of the mathematics of quantum field theory and featuring end-of-chapter quizzes and a final exam to test your knowledge, this book will teach you the fundamentals of this theoretical framework in no time at all. This fast and easy guide offers: Numerous figures to illustrate key concepts Sample equations with worked solutions Coverage of quantum numbers Details on the Dirac equation, the Feynman rules, and the Higgs mechanism A time-saving approach to performing better on an exam or at work Simple enough for a beginner, but challenging enough for an advanced student, Quantum Field Theory Demystified is your shortcut to understanding this fascinating area of physics.
This work is the first systematic study of all possible conformally covariant differential operators transforming differential forms on a Riemannian manifold X into those on a submanifold Y with focus on the model space (X, Y) = (Sn, Sn-1). The authors give a complete classification of all such conformally covariant differential operators, and find their explicit formulæ in the flat coordinates in terms of basic operators in differential geometry and classical hypergeometric polynomials. Resulting families of operators are natural generalizations of the Rankin–Cohen brackets for modular forms and Juhl's operators from conformal holography. The matrix-valued factorization identities among all possible combinations of conformally covariant differential operators are also established. The main machinery of the proof relies on the "F-method" recently introduced and developed by the authors. It is a general method to construct intertwining operators between C∞-induced representations or to find singular vectors of Verma modules in the context of branching rules, as solutions to differential equations on the Fourier transform side. The book gives a new extension of the F-method to the matrix-valued case in the general setting, which could be applied to other problems as well. This book offers a self-contained introduction to the analysis of symmetry breaking operators for infinite-dimensional representations of reductive Lie groups. This feature will be helpful for active scientists and accessible to graduate students and young researchers in differential geometry, representation theory, and theoretical physics.
The elucidation of reaction mechanisms generally requires the carefully designed control of molecular symmetry to distinguish between the many possible reaction pathways. Making and Breaking Symmetry in Chemistry emphasises the crucial role played by symmetry in modern synthetic chemistry. After discussion of a number of famous classical experiments, the advances brought about by the introduction of new techniques, in particular NMR spectroscopy, are exemplified in numerous cases taken from the recent literature. Experimental verification of many of the predictions made in Woodward and Hoffmann's explication of the Conservation of Orbital Symmetry are described. Applications that involve the breaking of molecular symmetry to resolve these and other mechanistic problems in organic, inorganic and organometallic chemistry are presented in the first sections of the book, together with many examples of the detection of hitherto hidden rearrangement processes. Subsequently, under the aegis of making molecular symmetry, examples of the preparation of highly symmetrical molecules found in the organic, organometallic or inorganic domains are discussed. These include Platonic hydrocarbons or boranes, tetrahedranes, cubanes, prismanes, dodecahedrane, fullerene fragments such as corannulene, sumanene or semibuckminsterfullerene, and other systems of unusual geometries or bonding characteristics (Möbius strips, molecular brakes and gears, Chauvin's carbomers, Fitjer's rotanes, persubstituted rings, metal-metal multiple bonds, etc.). The text also contains vignettes of many of the scientists who made these major advances, as well as short sections that briefly summarise key features of important topics that underpin the more descriptive material. These include some aspects of chirality, NMR spectroscopy, and the use of isotopic substitution to break molecular symmetry. A brief appendix on point group symmetry and nomenclature is also helpfully provided.
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.
