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Symmetries, coupled with the mathematical concept of group theory, are an essential conceptual backbone in the formulation of quantum field theories capable of describing the world of elementary particles. This primer is an introduction to and survey of the underlying concepts and structures needed in order to understand and handle these powerful tools. Specifically, in Part I of the book the symmetries and related group theoretical structures of the Minkowskian space-time manifold are analyzed, while Part II examines the internal symmetries and their related unitary groups, where the interactions between fundamental particles are encoded as we know them from the present standard model of particle physics. This book, based on several courses given by the authors, addresses advanced graduate students and non-specialist researchers wishing to enter active research in the field, and having a working knowledge of classical field theory and relativistic quantum mechanics. Numerous end-of-chapter problems and their solutions will facilitate the use of this book as self-study guide or as course book for topical lectures.
While theoretical particle physics is an extraordinarily fascinating field, the incredibly fast pace at which it moves along, combined with the huge amount of background information necessary to perform cutting edge research, poses a formidable challenge for graduate students. This book represents the first in a series designed to assist students in the process of transitioning from coursework to research in particle physics. Rather than reading literally dozens of physics and mathematics texts, trying to assimilate the countless ideas, translate notations and perspectives, and see how it all fits together to get a holistic understanding, this series provides a detailed overview of the major mathematical and physical ideas in theoretical particle physics. Ultimately the ideas will be presented in a unified, consistent, holistic picture, where each topic is built firmly on what has come before, and all topics are related in a clear and intuitive way. This introductory text on quantum field theory and particle physics provides both a self-contained and complete introduction to not only the necessary physical ideas, but also a complete introduction to the necessary mathematical tools. Assuming minimal knowledge of undergraduate physics and mathematics, this book lays both the mathematical and physical groundwork with clear, intuitive explanations and plenty of examples. The book then continues with an exposition of the Standard Model of Particle Physics, the theory that currently seems to explain the universe apart from gravity. Furthermore, this book was written as a primer for the more advanced mathematical and physical ideas to come later in this series.
An understanding of the properties and interactions of the elementary particles is an essential prerequisite of research work in high energy physics. Much progress in the subject has been achieved with the aid of symmetry principles. In this 1980 book the concept of symmetry or invariance is employed as a unifying theme. Using a careful explanation of the mathematical formalism and with many applications to particular cases, the authors introduce the reader to the symmetry schemes which dominate the world of the particle physicist. The presentation will also appeal to mathematicians and physicists in other fields who are interested in the applications of the general principles of symmetry. After a brief survey of the particles and a review of the relevant quantum mechanics, the principal symmetries are studied in turn. Some technical points are relegated to appendices and the book contains extensive references.
This is a textbook that derives the fundamental theories of physics from symmetry. It starts by introducing, in a completely self-contained way, all mathematical tools needed to use symmetry ideas in physics. Thereafter, these tools are put into action and by using symmetry constraints, the fundamental equations of Quantum Mechanics, Quantum Field Theory, Electromagnetism, and Classical Mechanics are derived. As a result, the reader is able to understand the basic assumptions behind, and the connections between the modern theories of physics. The book concludes with first applications of the previously derived equations. Thanks to the input of readers from around the world, this second edition has been purged of typographical errors and also contains several revised sections with improved explanations.
This book will explain how group theory underpins some of the key features of particle physics. It will examine symmetries and conservation laws in quantum mechanics and relate these to groups of transformations. Group theory provides the language for describing how particles (and in particular, their quantum numbers) combine. This provides understanding of hadronic physics as well as physics beyond the Standard Model. The symmetries of the Standard Model associated with the Electroweak and Strong (QCD) forces are described by the groups U(1), SU(2) and SU(3). The properties of these groups are examined and the relevance to particle physics is discussed.Stephen Haywood, author of Symmetries And Conservation Laws In Particle Physics, explains how his book can help experimental physicists and PhD students understand group theory and particle physics in our new video View the interview at http: //www.youtube.com/watch'v=jbQk78TBLS
Over the course of the last century it has become clear that both elementary particle physics and relativity theories are based on the notion of symmetries. These symmetries become manifest in that the "laws of nature" are invariant under spacetime transformations and/or gauge transformations. The consequences of these symmetries were analyzed as early as in 1918 by Emmy Noether on the level of action functionals. Her work did not receive due recognition for nearly half a century, but can today be understood as a recurring theme in classical mechanics, electrodynamics and special relativity, Yang-Mills type quantum field theories, and in general relativity. As a matter of fact, as shown in this monograph, many aspects of physics can be derived solely from symmetry considerations. This substantiates the statement of E.P. Wigner "... if we knew all the laws of nature, or the ultimate Law of nature, the invariance properties of these laws would not furnish us new information." Thanks to Wigner we now also understand the implications of quantum physics and symmetry considerations: Poincare invariance dictates both the characteristic properties of particles (mass, spin, ...) and the wave equations of spin 0, 1/2, 1, ... objects. Further, the work of C.N. Yang and R. Mills reveals the consequences of internal symmetries as exemplified in the symmetry group of elementary particle physics. Given this pivotal role of symmetries it is thus not surprising that current research in fundamental physics is to a great degree motivated and inspired by considerations of symmetry. The treatment of symmetries in this monograph ranges from classical physics to now well-established theories of fundamental interactions, to the latest research on unified theories and quantum gravity.
These lecture notes provide a tutorial review of non-Abelian discrete groups and show some applications to issues in physics where discrete symmetries constitute an important principle for model building in particle physics. While Abelian discrete symmetries are often imposed in order to control couplings for particle physics - in particular model building beyond the standard model - non-Abelian discrete symmetries have been applied to understand the three-generation flavor structure in particular. Indeed, non-Abelian discrete symmetries are considered to be the most attractive choice for the flavor sector: model builders have tried to derive experimental values of quark and lepton masses, and mixing angles by assuming non-Abelian discrete flavor symmetries of quarks and leptons, yet, lepton mixing has already been intensively discussed in this context, as well. The possible origins of the non-Abelian discrete symmetry for flavors is another topic of interest, as they can arise from an underlying theory - e.g. the string theory or compactification via orbifolding – thereby providing a possible bridge between the underlying theory and the corresponding low-energy sector of particle physics. This text explicitly introduces and studies the group-theoretical aspects of many concrete groups and shows how to derive conjugacy classes, characters, representations, and tensor products for these groups (with a finite number) when algebraic relations are given, thereby enabling readers to apply this to other groups of interest.
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.
Unitary Symmetry and Elementary Particles discusses the role of symmetry in elementary particle physics. The book reviews the theory of abstract groups and group representations including Eigenstates, cosets, conjugate classes, unitary vector spaces, unitary representations, multiplets, and conservation laws. The text also explains the concept of Young Diagrams or Young Tableaux to prove the basis functions of the unitary irreducible representations of the unitary group SU(n). The book defines Lie groups, Lie algebras, and gives some examples of these groups. The basis vectors of irreducible unitary representations of Lie groups constitute a multiplet, which according to Racah (1965) and Behrends et al. (1962) can have properties of weights. The text also explains the properties of Clebsch-Gordan coefficients and the Wigner-Eckart theorem. SU(3) multiplets have members classified as hadrons (strongly interacting particles), of which one characteristic show that the mass differences of these members have some regular properties. The Gell-Mann and Ne-eman postulate also explains another characteristic peculiar to known multiplets. The book describes the quark model, as well as, the uses of the variants of the quark model. This collection is suitable for researchers and scientists in the field of applied mathematics, nuclear physics, and quantum mechanics.