Group Theory In Physics: A Practitioner's Guide PDF Download

Author: R Campoamor Strursberg
Publisher: World Scientific
ISBN: 9813273623
Category : Science
Languages : en
Pages : 759

View

Book Description
'The book contains a lot of examples, a lot of non-standard material which is not included in many other books. At the same time the authors manage to avoid numerous cumbersome calculations … It is a great achievement that the authors found a balance.'zbMATHThis book presents the study of symmetry groups in Physics from a practical perspective, i.e. emphasising the explicit methods and algorithms useful for the practitioner and profusely illustrating by examples.The first half reviews the algebraic, geometrical and topological notions underlying the theory of Lie groups, with a review of the representation theory of finite groups. The topic of Lie algebras is revisited from the perspective of realizations, useful for explicit computations within these groups. The second half is devoted to applications in physics, divided into three main parts — the first deals with space-time symmetries, the Wigner method for representations and applications to relativistic wave equations. The study of kinematical algebras and groups illustrates the properties and capabilities of the notions of contractions, central extensions and projective representations. Gauge symmetries and symmetries in Particle Physics are studied in the context of the Standard Model, finishing with a discussion on Grand-Unified Theories.

Author: Rutwig Campoamor-Stursberg
Publisher: World Scientific Publishing Company
ISBN: 9789813273603
Category : Group theory
Languages : en
Pages : 0

View

Book Description
This book presents the study of symmetry groups in Physics from a practical perspective, i.e. emphasising the explicit methods and algorithms useful for the practitioner and profusely illustrating by examples. The first half reviews the algebraic, geometrical and topological notions underlying the theory of Lie groups, with a review of the representation theory of finite groups. The topic of Lie algebras is revisited from the perspective of realizations, useful for explicit computations within these groups. The second half is devoted to applications in physics, divided into three main parts -- the first deals with space-time symmetries, the Wigner method for representations and applications to relativistic wave equations. The study of kinematical algebras and groups illustrates the properties and capabilities of the notions of contractions, central extensions and projective representations. Gauge symmetries and symmetries in Particle Physics are studied in the context of the Standard Model, finishing with a discussion on Grand-Unified Theories.

Author: Herbi K. Dreiner
Publisher: Cambridge University Press
ISBN: 1009347535
Category : Science
Languages : en
Pages : 1031

View

Book Description
Supersymmetry is an extension of the successful Standard Model of particle physics; it relies on the principle that fermions and bosons are related by a symmetry, leading to an elegant predictive structure for quantum field theory. This textbook provides a comprehensive and pedagogical introduction to supersymmetry and spinor techniques in quantum field theory. By utilising the two-component spinor formalism for fermions, the authors provide many examples of practical calculations relevant for collider physics signatures, anomalies, and radiative corrections. They present in detail the component field and superspace formulations of supersymmetry and explore related concepts, including the theory of extended Higgs sectors, models of grand unification, and the origin of neutrino masses. Numerous exercises are provided at the end of each chapter. Aimed at graduate students and researchers, this volume provides a clear and unified treatment of theoretical concepts that are at the frontiers of high energy particle physics.

Author: Vladimir Dobrev
Publisher: Springer Nature
ISBN: 9811947511
Category : Mathematics
Languages : en
Pages : 526

View

Book Description
This volume presents modern trends in the area of symmetries and their applications based on contributions to the Workshop "Lie Theory and Its Applications in Physics" held in Sofia, Bulgaria (on-line) in June 2021. Traditionally, Lie theory is a tool to build mathematical models for physical systems. Recently, the trend is towards geometrization of the mathematical description of physical systems and objects. A geometric approach to a system yields in general some notion of symmetry which is very helpful in understanding its structure. Geometrization and symmetries are meant in their widest sense, i.e., representation theory, algebraic geometry, number theory, infinite-dimensional Lie algebras and groups, superalgebras and supergroups, groups and quantum groups, noncommutative geometry, symmetries of linear and nonlinear partial differential operators, special functions, and others. Furthermore, the necessary tools from functional analysis are included. This is a big interdisciplinary and interrelated field. The topics covered in this Volume are the most modern trends in the field of the Workshop: Representation Theory, Symmetries in String Theories, Symmetries in Gravity Theories, Supergravity, Conformal Field Theory, Integrable Systems, Quantum Computing and Deep Learning, Entanglement, Applications to Quantum Theory, Exceptional quantum algebra for the standard model of particle physics, Gauge Theories and Applications, Structures on Lie Groups and Lie Algebras. This book is suitable for a broad audience of mathematicians, mathematical physicists, and theoretical physicists, including researchers and graduate students interested in Lie Theory.

Author: Young Suh Kim
Publisher: World Scientific
ISBN: 9813237724
Category : Science
Languages : en
Pages : 205

View

Book Description
Einstein's energy-momentum relation is applicable to particles of all speeds, including the particle at rest and the massless particle moving with the speed of light. If one formula or formalism is applicable to all speeds, we say it is 'Lorentz-covariant.' As for the internal space-time symmetries, there does not appear to be a clear way to approach this problem. For a particle at rest, there are three spin degrees of freedom. For a massless particle, there are helicity and gauge degrees of freedom. The aim of this book is to present one Lorentz-covariant picture of these two different space-time symmetries. Using the same mathematical tool, it is possible to give a Lorentz-covariant picture of Gell-Mann's quark model for the proton at rest and Feynman's parton model for the fast-moving proton. The mathematical formalism for these aspects of the Lorentz covariance is based on two-by-two matrices and harmonic oscillators which serve as two basic scientific languages for many different branches of physics. It is pointed out that the formalism presented in this book is applicable to various aspects of optical sciences of current interest.

Author: Rutwig Campoamor-Stursberg
Publisher:
ISBN: 9789811221279
Category :
Languages : en
Pages : 0

View

Book Description
"The book contains a lot of examples, a lot of non-standard material which is not included in many other books. At the same time the authors manage to avoid numerous cumbersome calculations ... It is a great achievement that the authors found a balance." zbMATH This book presents the study of symmetry groups in Physics from a practical perspective, i.e. emphasising the explicit methods and algorithms useful for the practitioner and profusely illustrating by examples. The first half reviews the algebraic, geometrical and topological notions underlying the theory of Lie groups, with a review of the representation theory of finite groups. The topic of Lie algebras is revisited from the perspective of realizations, useful for explicit computations within these groups. The second half is devoted to applications in physics, divided into three main parts -- the first deals with space-time symmetries, the Wigner method for representations and applications to relativistic wave equations. The study of kinematical algebras and groups illustrates the properties and capabilities of the notions of contractions, central extensions and projective representations. Gauge symmetries and symmetries in Particle Physics are studied in the context of the Standard Model, finishing with a discussion on Grand-Unified Theories.

Author: Predrag Cvitanović
Publisher: Princeton University Press
ISBN: 1400837677
Category : Mathematics
Languages : en
Pages : 278

View

Book Description
If classical Lie groups preserve bilinear vector norms, what Lie groups preserve trilinear, quadrilinear, and higher order invariants? Answering this question from a fresh and original perspective, Predrag Cvitanovic takes the reader on the amazing, four-thousand-diagram journey through the theory of Lie groups. This book is the first to systematically develop, explain, and apply diagrammatic projection operators to construct all semi-simple Lie algebras, both classical and exceptional. The invariant tensors are presented in a somewhat unconventional, but in recent years widely used, "birdtracks" notation inspired by the Feynman diagrams of quantum field theory. Notably, invariant tensor diagrams replace algebraic reasoning in carrying out all group-theoretic computations. The diagrammatic approach is particularly effective in evaluating complicated coefficients and group weights, and revealing symmetries hidden by conventional algebraic or index notations. The book covers most topics needed in applications from this new perspective: permutations, Young projection operators, spinorial representations, Casimir operators, and Dynkin indices. Beyond this well-traveled territory, more exotic vistas open up, such as "negative dimensional" relations between various groups and their representations. The most intriguing result of classifying primitive invariants is the emergence of all exceptional Lie groups in a single family, and the attendant pattern of exceptional and classical Lie groups, the so-called Magic Triangle. Written in a lively and personable style, the book is aimed at researchers and graduate students in theoretical physics and mathematics.

Author: A. Zee
Publisher: Princeton University Press
ISBN: 1400881188
Category : Science
Languages : en
Pages : 632

View

Book Description
A concise, modern textbook on group theory written especially for physicists Although group theory is a mathematical subject, it is indispensable to many areas of modern theoretical physics, from atomic physics to condensed matter physics, particle physics to string theory. In particular, it is essential for an understanding of the fundamental forces. Yet until now, what has been missing is a modern, accessible, and self-contained textbook on the subject written especially for physicists. Group Theory in a Nutshell for Physicists fills this gap, providing a user-friendly and classroom-tested text that focuses on those aspects of group theory physicists most need to know. From the basic intuitive notion of a group, A. Zee takes readers all the way up to how theories based on gauge groups could unify three of the four fundamental forces. He also includes a concise review of the linear algebra needed for group theory, making the book ideal for self-study. Provides physicists with a modern and accessible introduction to group theory Covers applications to various areas of physics, including field theory, particle physics, relativity, and much more Topics include finite group and character tables; real, pseudoreal, and complex representations; Weyl, Dirac, and Majorana equations; the expanding universe and group theory; grand unification; and much more The essential textbook for students and an invaluable resource for researchers Features a brief, self-contained treatment of linear algebra An online illustration package is available to professors Solutions manual (available only to professors)

Author: Ernest L. Rossi
Publisher: Crown House Publishing Ltd
ISBN: 1785832913
Category : Psychology
Languages : en
Pages : 405

View

Book Description
Richard Hill and Ernest L. Rossi's The Practitioner's Guide to Mirroring Hands: A Client-Responsive Therapy that Facilitates Natural Problem-Solving and Mind Body Healing describes in detail how Mirroring Hands is conducted, and explores the framework of knowledge and understanding that surrounds and supports its therapeutic process. Foreword by Jeffrey K. Zeig, Ph.D. In this instructive and illuminating manual, Hill and Rossi show you how Mirroring Hands enables clients to unlock their problem-solving and mind body healing capacities to arrive at a resolution in a way that many other therapies might not. The authors offer expert guidance as to its client-responsive applications and differentiate seven variations of the technique in order to give the practitioner confidence and comfort in their ability to work within and around the possibilities presented while in session. Furthermore, Hill and Rossi punctuate their description of how Mirroring Hands is conducted with a range of illustrative casebook examples and stage-by-stage snapshots of the therapy in action: providing scripted language prompts and images of a client's hand movement that demonstrate the processes behind the technique as it takes the client from disruption into the therapeutic; and from there to integration, resolution, and a state of well-being. This book begins by tracing the emergence of the Mirroring Hands approach from its origins in Rossi's studies and experiences with Milton H. Erickson and by presenting a transcription of an insightful discussion between Rossi and Hill as they challenge some of the established ways in which we approach psychotherapy, health, and well-being. Building upon this exchange of ideas, the authors define and demystify the nature of complex, non-linear systems and skillfully unpack the three key elements of induction to therapeutic consciousness focused attention, curiosity, and nascent confidence in a section dedicated to preparing the client for therapy. Hill and Rossi supply guidance for the therapist through explanation of therapeutic dialogue's non-directive language principles, and through exploration of the four-stage cycle that facilitates the client's capacity to access their natural problem-solving and mind body healing. The advocate Mirroring Hands as not only a therapeutic technique, but also for all practitioners engaged in solution-focused therapy. Through its enquiry into the vital elements of client-cue observation, symptom-scaling, and rapport-building inherent in the therapist/client relationship, this book shares great wisdom and insight that will help the practitioner become more attuned to their clients' inner worlds and communication patterns. Hill and Rossi draw on a wealth of up-to-date neuroscientific research and academic theory to help bridge the gap between therapy's intended outcomes and its measured neurological effects, and, towards the book's close, also open the door to the study of quantum field theory to inspire the reader's curiosity in this fascinating topic. An ideal progression for those engaged in mindfulness and meditation, this book is the first book on the subject specially written for all mental health practitioners and is suitable for students of counseling, psychotherapy, psychology, and hypnotherapy, as well as anyone in professional practice.

Author: Susan A. Wheelan
Publisher: SAGE
ISBN: 9780761929581
Category : Business & Economics
Languages : en
Pages : 616

View

Book Description
Organized into six practical sections relating theory to application from an historical perspective, this text offers contributions from international scholars and practitioners who reflect the diversity of this field.