An Introduction to Tensors and Group Theory for Physicists

An Introduction to Tensors and Group Theory for Physicists Author Nadir Jeevanjee
ISBN-10 9783319147949
Year 2015-03-11
Pages 305
Language en
Publisher Birkhäuser
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The second edition of this highly praised textbook provides an introduction to tensors, group theory, and their applications in classical and quantum physics. Both intuitive and rigorous, it aims to demystify tensors by giving the slightly more abstract but conceptually much clearer definition found in the math literature, and then connects this formulation to the component formalism of physics calculations. New pedagogical features, such as new illustrations, tables, and boxed sections, as well as additional “invitation” sections that provide accessible introductions to new material, offer increased visual engagement, clarity, and motivation for students. Part I begins with linear algebraic foundations, follows with the modern component-free definition of tensors, and concludes with applications to physics through the use of tensor products. Part II introduces group theory, including abstract groups and Lie groups and their associated Lie algebras, then intertwines this material with that of Part I by introducing representation theory. Examples and exercises are provided in each chapter for good practice in applying the presented material and techniques. Prerequisites for this text include the standard lower-division mathematics and physics courses, though extensive references are provided for the motivated student who has not yet had these. Advanced undergraduate and beginning graduate students in physics and applied mathematics will find this textbook to be a clear, concise, and engaging introduction to tensors and groups. Reviews of the First Edition “[P]hysicist Nadir Jeevanjee has produced a masterly book that will help other physicists understand those subjects [tensors and groups] as mathematicians understand them... From the first pages, Jeevanjee shows amazing skill in finding fresh, compelling words to bring forward the insight that animates the modern mathematical view...[W]ith compelling force and clarity, he provides many carefully worked-out examples and well-chosen specific problems... Jeevanjee’s clear and forceful writing presents familiar cases with a freshness that will draw in and reassure even a fearful student. [This] is a masterpiece of exposition and explanation that would win credit for even a seasoned author.” —Physics Today "Jeevanjee’s [text] is a valuable piece of work on several counts, including its express pedagogical service rendered to fledgling physicists and the fact that it does indeed give pure mathematicians a way to come to terms with what physicists are saying with the same words we use, but with an ostensibly different meaning. The book is very easy to read, very user-friendly, full of examples...and exercises, and will do the job the author wants it to do with style.” —MAA Reviews

Group Theory in the Bedroom and Other Mathematical Diversions

Group Theory in the Bedroom  and Other Mathematical Diversions Author Brian Hayes
ISBN-10 1429938579
Year 2008-04-01
Pages 288
Language en
Publisher Hill and Wang
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An Award-Winning Essayist Plies His Craft Brian Hayes is one of the most accomplished essayists active today—a claim supported not only by his prolific and continuing high-quality output but also by such honors as the National Magazine Award for his commemorative Y2K essay titled "Clock of Ages," published in the November/December 1999 issue of The Sciences magazine. (The also-rans that year included Tom Wolfe, Verlyn Klinkenborg, and Oliver Sacks.) Hayes's work in this genre has also appeared in such anthologies as The Best American Magazine Writing, The Best American Science and Nature Writing, and The Norton Reader. Here he offers us a selection of his most memorable and accessible pieces—including "Clock of Ages"—embellishing them with an overall, scene-setting preface, reconfigured illustrations, and a refreshingly self-critical "Afterthoughts" section appended to each essay.

Groups

Groups Author R. P. Burn
ISBN-10 0521347939
Year 1987-09-03
Pages 242
Language en
Publisher Cambridge University Press
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Following the same successful approach as Dr. Burn's previous book on number theory, this text consists of a carefully constructed sequence of questions that will enable the reader, through participation, to study all the group theory covered by a conventional first university course. An introduction to vector spaces, leading to the study of linear groups, and an introduction to complex numbers, leading to the study of Möbius transformations and stereographic projection, are also included. Quaternions and their relationships to 3-dimensional isometries are covered, and the climax of the book is a study of the crystallographic groups, with a complete analysis of these groups in two dimensions.

Topics in Geometric Group Theory

Topics in Geometric Group Theory Author Pierre de la Harpe
ISBN-10 0226317196
Year 2000-10-15
Pages 310
Language en
Publisher University of Chicago Press
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In this book, Pierre de la Harpe provides a concise and engaging introduction to geometric group theory, a new method for studying infinite groups via their intrinsic geometry that has played a major role in mathematics over the past two decades. A recognized expert in the field, de la Harpe adopts a hands-on approach, illustrating key concepts with numerous concrete examples. The first five chapters present basic combinatorial and geometric group theory in a unique and refreshing way, with an emphasis on finitely generated versus finitely presented groups. In the final three chapters, de la Harpe discusses new material on the growth of groups, including a detailed treatment of the "Grigorchuk group." Most sections are followed by exercises and a list of problems and complements, enhancing the book's value for students; problems range from slightly more difficult exercises to open research problems in the field. An extensive list of references directs readers to more advanced results as well as connections with other fields.

Group Theory

Group Theory Author Predrag Cvitanović
ISBN-10 0691118361
Year 2008-07-21
Pages 273
Language en
Publisher Princeton University Press
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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.

Fundamentals of Group Theory

Fundamentals of Group Theory Author Steven Roman
ISBN-10 9780817683016
Year 2011-10-26
Pages 380
Language en
Publisher Springer Science & Business Media
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Fundamentals of Group Theory provides a comprehensive account of the basic theory of groups. Both classic and unique topics in the field are covered, such as an historical look at how Galois viewed groups, a discussion of commutator and Sylow subgroups, and a presentation of Birkhoff’s theorem. Written in a clear and accessible style, the work presents a solid introduction for students wishing to learn more about this widely applicable subject area. This book will be suitable for graduate courses in group theory and abstract algebra, and will also have appeal to advanced undergraduates. In addition it will serve as a valuable resource for those pursuing independent study. Group Theory is a timely and fundamental addition to literature in the study of groups.

Visual Complex Functions

Visual Complex Functions Author Elias Wegert
ISBN-10 9783034801805
Year 2012-08-30
Pages 360
Language en
Publisher Springer Science & Business Media
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This book provides a systematic introduction to functions of one complex variable. Its novel feature is the consistent use of special color representations – so-called phase portraits – which visualize functions as images on their domains. Reading Visual Complex Functions requires no prerequisites except some basic knowledge of real calculus and plane geometry. The text is self-contained and covers all the main topics usually treated in a first course on complex analysis. With separate chapters on various construction principles, conformal mappings and Riemann surfaces it goes somewhat beyond a standard programme and leads the reader to more advanced themes. In a second storyline, running parallel to the course outlined above, one learns how properties of complex functions are reflected in and can be read off from phase portraits. The book contains more than 200 of these pictorial representations which endow individual faces to analytic functions. Phase portraits enhance the intuitive understanding of concepts in complex analysis and are expected to be useful tools for anybody working with special functions – even experienced researchers may be inspired by the pictures to new and challenging questions. Visual Complex Functions may also serve as a companion to other texts or as a reference work for advanced readers who wish to know more about phase portraits.

Group Theory in a Nutshell for Physicists

Group Theory in a Nutshell for Physicists Author A. Zee
ISBN-10 9781400881185
Year 2016-03-29
Pages 632
Language en
Publisher Princeton University Press
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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)

Visual Complex Analysis

Visual Complex Analysis Author Tristan Needham
ISBN-10 0198534469
Year 1998
Pages 592
Language en
Publisher Oxford University Press
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Now available in paperback, this successful radical approach to complex analysis replaces the standard calculational arguments with new geometric ones. With several hundred diagrams, and far fewer prerequisites than usual, this is the first visual intuitive introduction to complex analysis. Although designed for use by undergraduates in mathematics and science, the novelty of the approach will also interest professional mathematicians.

Group Theory for Chemists

Group Theory for Chemists Author Kieran C. Molloy
ISBN-10 1904275168
Year 2004-01-01
Pages 146
Language en
Publisher Horwood Publishing
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Concise undergraduate course text with a pictorial approach, deals with basics of group theory and its application to analysis of vibrational spectra, and a molecular orbital description of bonding. Developed from a course that the author has taught for many years, it links the topics to ligand field theory and properties of transition metal complexes and other themes within inorganic chemistry. The author stresses the importance of problem solving, and has therefore interspersed self-assessment questions to reinforce material at key stages in the text. There are problem exercises at the end of most chapters, with solutions and tutorial hints avoiding heavy mathematics.

Visual Computing for Medicine

Visual Computing for Medicine Author Bernhard Preim
ISBN-10 9780124159792
Year 2013-11-07
Pages 836
Language en
Publisher Newnes
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Visual Computing for Medicine, Second Edition, offers cutting-edge visualization techniques and their applications in medical diagnosis, education, and treatment. The book includes algorithms, applications, and ideas on achieving reliability of results and clinical evaluation of the techniques covered. Preim and Botha illustrate visualization techniques from research, but also cover the information required to solve practical clinical problems. They base the book on several years of combined teaching and research experience. This new edition includes six new chapters on treatment planning, guidance and training; an updated appendix on software support for visual computing for medicine; and a new global structure that better classifies and explains the major lines of work in the field. Complete guide to visual computing in medicine, fully revamped and updated with new developments in the field Illustrated in full color Includes a companion website offering additional content for professors, source code, algorithms, tutorials, videos, exercises, lessons, and more

Distributions

Distributions Author J.J. Duistermaat
ISBN-10 0817646752
Year 2010-08-09
Pages 445
Language en
Publisher Springer Science & Business Media
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This textbook is an application-oriented introduction to the theory of distributions, a powerful tool used in mathematical analysis. The treatment emphasizes applications that relate distributions to linear partial differential equations and Fourier analysis problems found in mechanics, optics, quantum mechanics, quantum field theory, and signal analysis. The book is motivated by many exercises, hints, and solutions that guide the reader along a path requiring only a minimal mathematical background.

Driver Distraction

Driver Distraction Author Kristie Young
ISBN-10 1420007491
Year 2008-10-15
Pages 672
Language en
Publisher CRC Press
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A Practical Resource for Understanding, Preventing, and Managing Driver Distraction It is estimated that up to 23 percent of crashes and near-crashes are caused by driver distraction, and these figures will likely increase as more and more distractions, both inside and outside the vehicle, compete for driver attention. Driver Distraction: Theory, Effects, and Mitigation gives a comprehensive overview of this issue, outlining the underlying theory of distraction, its effects on driving performance and safety, strategies for mitigating its effects, and directions for future research. It also brings together the wide array of literature on the topic into one, all-inclusive volume. Includes Recommendations for Managing Distractions in the Technological Age This comprehensive volume reviews the full range of distracting activities that occur while driving, and available ergonomic methods, guidelines, and checklists for the measurement and mitigation of driver distraction. It also recommends ways to manage distraction through enhanced data collection and analysis, driver education and training, driver licensing, legislation and enforcement, vehicle design, road design, company policies, and future research. Beneficial for a broad audience, including: Vehicle manufacturers Road transport authorities and safety agencies Traffic and transport engineers Automotive equipment manufacturers and suppliers Company safety managers Standards organizations Transport safety research agencies This work comes at a critical time when road safety authorities are just beginning to recognize the importance of driver distraction as a road safety issue. With balanced and practical guidance, it aims to prevent driver distraction from escalating into an even more significant problem.

Visual Methods in Psychology

Visual Methods in Psychology Author Paula Reavey
ISBN-10 9781136812576
Year 2012-03-29
Pages 416
Language en
Publisher Routledge
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This comprehensive volume provides an unprecedented illustration of the potential for visual methods in psychology. Each chapter explores the set of theoretical, methodological, as well as ethical and analytical issues that shape the ways in which visual qualitative research is conducted in psychology. Using a variety of forms of visual data, including photography, documentary film-making, drawing, internet media, model making and collages, each author endeavors to broaden the scope for understanding experience and subjectivity, using visual qualitative methods. The contributors to this volume work within a variety of traditions including narrative psychology, personal construct theory, discursive psychology and conversation analysis, phenomenology and psychoanalysis. Each addresses how a particular visual approach has contributed to existing social and psychological theory in their topic area, and clearly outline how they carried out their specific research project. The contributors draw on qualitative sources of verbal data, such as spoken interview, diaries and naturalistic conversation alongside their use of visual material. This book provides a unique insight into the potential for combining methods in order to create new multi-modal methodologies, and it presents and analyses these with psychology specific questions in mind. The range of topics covered includes sexuality, identity, group processes, child development, forensic psychology, race, and gender, making this volume a vital contribution to psychology, sociology and gender studies.