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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.
Galileo Unbound traces the journey that brought us from Galileo's law of free fall to today's geneticists measuring evolutionary drift, entangled quantum particles moving among many worlds, and our lives as trajectories traversing a health space with thousands of dimensions. Remarkably, common themes persist that predict the evolution of species as readily as the orbits of planets or the collapse of stars into black holes. This book tells the history of spaces of expanding dimension and increasing abstraction and how they continue today to give new insight into the physics of complex systems. Galileo published the first modern law of motion, the Law of Fall, that was ideal and simple, laying the foundation upon which Newton built the first theory of dynamics. Early in the twentieth century, geometry became the cause of motion rather than the result when Einstein envisioned the fabric of space-time warped by mass and energy, forcing light rays to bend past the Sun. Possibly more radical was Feynman's dilemma of quantum particles taking all paths at once — setting the stage for the modern fields of quantum field theory and quantum computing. Yet as concepts of motion have evolved, one thing has remained constant, the need to track ever more complex changes and to capture their essence, to find patterns in the chaos as we try to predict and control our world.
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.
INSTANT NEW YORK TIMES BESTSELLER “Most appealing... technical accuracy and lightness of tone... Impeccable.”—Wall Street Journal “A porthole into another world.”—Scientific American “Brings science dissemination to a new level.”—Science The most trusted explainer of the most mind-boggling concepts pulls back the veil of mystery that has too long cloaked the most valuable building blocks of modern science. Sean Carroll, with his genius for making complex notions entertaining, presents in his uniquely lucid voice the fundamental ideas informing the modern physics of reality. Physics offers deep insights into the workings of the universe but those insights come in the form of equations that often look like gobbledygook. Sean Carroll shows that they are really like meaningful poems that can help us fly over sierras to discover a miraculous multidimensional landscape alive with radiant giants, warped space-time, and bewilderingly powerful forces. High school calculus is itself a centuries-old marvel as worthy of our gaze as the Mona Lisa. And it may come as a surprise the extent to which all our most cutting-edge ideas about black holes are built on the math calculus enables. No one else could so smoothly guide readers toward grasping the very equation Einstein used to describe his theory of general relativity. In the tradition of the legendary Richard Feynman lectures presented sixty years ago, this book is an inspiring, dazzling introduction to a way of seeing that will resonate across cultural and generational boundaries for many years to come.
Based on the author’s well-established courses, Group Theory for the Standard Model of Particle Physics and Beyond explores the use of symmetries through descriptions of the techniques of Lie groups and Lie algebras. The text develops the models, theoretical framework, and mathematical tools to understand these symmetries. After linking symmetries with conservation laws, the book works through the mathematics of angular momentum and extends operators and functions of classical mechanics to quantum mechanics. It then covers the mathematical framework for special relativity and the internal symmetries of the standard model of elementary particle physics. In the chapter on Noether’s theorem, the author explains how Lagrangian formalism provides a natural framework for the quantum mechanical interpretation of symmetry principles. He then examines electromagnetic, weak, and strong interactions; spontaneous symmetry breaking; the elusive Higgs boson; and supersymmetry. He also introduces new techniques based on extending space–time into dimensions described by anticommuting coordinates. Designed for graduate and advanced undergraduate students in physics, this text provides succinct yet complete coverage of the group theory of the symmetries of the standard model of elementary particle physics. It will help students understand current knowledge about the standard model as well as the physics that potentially lies beyond the standard model.
This book brings together philosophical discussions of symmetry in physics, highlighting the main issues and controversies. It covers all the fundamental symmetries of modern physics, as well as discussing symmetry-breaking and general interpretational issues. For each topic, classic texts are followed by review articles and short commentaries.
This new edition of The Standard Model and Beyond presents an advanced introduction to the physics and formalism of the standard model and other non-abelian gauge theories. It provides a solid background for understanding supersymmetry, string theory, extra dimensions, dynamical symmetry breaking, and cosmology. In addition to updating all of the experimental and phenomenological results from the first edition, it contains a new chapter on collider physics; expanded discussions of Higgs, neutrino, and dark matter physics; and many new problems. The book first reviews calculational techniques in field theory and the status of quantum electrodynamics. It then focuses on global and local symmetries and the construction of non-abelian gauge theories. The structure and tests of quantum chromodynamics, collider physics, the electroweak interactions and theory, and the physics of neutrino mass and mixing are thoroughly explored. The final chapter discusses the motivations for extending the standard model and examines supersymmetry, extended gauge groups, and grand unification. Thoroughly covering gauge field theories, symmetries, and topics beyond the standard model, this text equips readers with the tools to understand the structure and phenomenological consequences of the standard model, to construct extensions, and to perform calculations at tree level. It establishes the necessary background for readers to carry out more advanced research in particle physics. Supplementary materials are provided on the author’s website and a solutions manual is available for qualifying instructors.
Supersymmetry represents the culmination of the search for fundamental symmetries that has dominated particle physics for 50 years. Traditionally, the constituents of matter (fermions) were regarded as different from the particles (bosons) transmitting the forces between them. In supersymmetry, fermions and bosons are unified. Intended for graduate students in particle physics, and researchers in experimental and phenomenological supersymmetry, this textbook, first published in 2007, provides a simple introduction to a previously formidably technical field. Its elementary, practical treatment brings readers to the frontier of contemporary research, in particular the experiments at the Large Hadron Collider. Theories are constructed through an intuitive 'trial and error' approach. Basic elements of spinor formalism and superfields are introduced, allowing readers to access more advanced treatments. Emphasis is placed on physical understanding, and on detailed derivations of important steps. Many short exercises are included, making for a valuable and accessible self-study tool.
This book is devoted to some recently developed techniques in quantum field theory (QFT), as well as to their main applications to different areas of parti cle physics. All together they are known as the effective or phenomenological Lagrangian formalism. Motivated by the enormous amount of work carried out in this field during the last years, our purpose when writing this book has been to give a modern and pedagogical exposition of the most relevant as pects of the topic. We hope that our efforts will be useful, both for graduated students in the search for a solid theoretical background in modern phe nomenology and for more experimented particle physicists willing to learn about this field or to start working on it. Even though we have tried to keep the book as self-contained as possible, it has been written assuming that the reader is familiar, at least, with the most basic concepts and techniques of QFT, gauge theories, the standard model (SM) and differential geometry, at the level of graduate studies. It is therefore possible that senior high-energy physicists may find the book too detailed and so they could probably omit several sections. The book is divided into two main parts and the appendices. In the first part we introduce the fundamentals of the effective Lagrangian formalism and other basic topics such as Ward identities, non-linear sigma models (NLSM), spontaneous symmetry breaking (SSB), anomalies, the SM symmetries, etc.
This book is an introduction to the concept of symmetries in electromagnetism and explicit symmetry breaking. It begins with a brief background on the origin of the concept of symmetry and its meaning in fields such as architecture, mathematics and physics. Despite the extensive developments of symmetry in these fields, it has yet to be applied to the context of classical electromagnetism and related engineering applications. This book unravels the beauty and excitement of this area to scientists and engineers.