The Search for Beauty in Modern Physics

Author: A. Zee

Publisher: Princeton University Press

ISBN: 1400874505

Category: Science

Page: 376

View: 8652

The concept of symmetry has widespread manifestations and many diverse applications—from architecture to mathematics to science. Yet, as twentieth-century physics has revealed, symmetry has a special, central role in nature, one that is occasionally and enigmatically violated. Fearful Symmetry brings the incredible discoveries of the juxtaposition of symmetry and asymmetry in contemporary physics within everyone's grasp. A. Zee, a distinguished physicist and skillful expositor, tells the exciting story of how contemporary theoretical physicists are following Einstein in their search for the beauty and simplicity of Nature. Animated by a sense of reverence and whimsy, Fearful Symmetry describes the majestic sweep and accomplishments of twentieth-century physics—one of the greatest chapters in the intellectual history of humankind.
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Author: Hermann Weyl

Publisher: Princeton University Press

ISBN: 1400874343

Category: Science

Page: 176

View: 1229

Symmetry is a classic study of symmetry in mathematics, the sciences, nature, and art from one of the twentieth century's greatest mathematicians. Hermann Weyl explores the concept of symmetry beginning with the idea that it represents a harmony of proportions, and gradually departs to examine its more abstract varieties and manifestations—as bilateral, translatory, rotational, ornamental, and crystallographic. Weyl investigates the general abstract mathematical idea underlying all these special forms, using a wealth of illustrations as support. Symmetry is a work of seminal relevance that explores the great variety of applications and importance of symmetry.
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Author: Matt Hawkins

Publisher: Image Comics

ISBN: N.A

Category: Comics & Graphic Novels

Page: 32

View: 1616

Utopia no more!
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Author: Ian Stewart

Publisher: OUP Oxford

ISBN: 0199651981

Category: Mathematics

Page: 160

View: 8273

Symmetry is an immensely important concept in mathematics and throughout the sciences. In this Very Short Introduction, Ian Stewart highlights the deep implications of symmetry and its important scientific applications across the entire subject.
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Exposing the Hidden Patterns of Numbers

Author: Avner Ash,Robert Gross

Publisher: Princeton University Press

ISBN: 1400837774

Category: Mathematics

Page: 312

View: 729

Mathematicians solve equations, or try to. But sometimes the solutions are not as interesting as the beautiful symmetric patterns that lead to them. Written in a friendly style for a general audience, Fearless Symmetry is the first popular math book to discuss these elegant and mysterious patterns and the ingenious techniques mathematicians use to uncover them. Hidden symmetries were first discovered nearly two hundred years ago by French mathematician évariste Galois. They have been used extensively in the oldest and largest branch of mathematics--number theory--for such diverse applications as acoustics, radar, and codes and ciphers. They have also been employed in the study of Fibonacci numbers and to attack well-known problems such as Fermat's Last Theorem, Pythagorean Triples, and the ever-elusive Riemann Hypothesis. Mathematicians are still devising techniques for teasing out these mysterious patterns, and their uses are limited only by the imagination. The first popular book to address representation theory and reciprocity laws, Fearless Symmetry focuses on how mathematicians solve equations and prove theorems. It discusses rules of math and why they are just as important as those in any games one might play. The book starts with basic properties of integers and permutations and reaches current research in number theory. Along the way, it takes delightful historical and philosophical digressions. Required reading for all math buffs, the book will appeal to anyone curious about popular mathematics and its myriad contributions to everyday life.
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Author: Leon M. Lederman,Christopher T. Hill

Publisher: Prometheus Books

ISBN: 1615920412

Category: Science

Page: 363

View: 9684

When scientists peer through a telescope at the distant stars in outer space or use a particle-accelerator to analyze the smallest components of matter, they discover that the same laws of physics govern the whole universe at all times and all places. Physicists call the eternal, ubiquitous constancy of the laws of physics symmetry. Symmetry is the basic underlying principle that defines the laws of nature and hence controls the universe. This all-important insight is one of the great conceptual breakthroughs in modern physics and is the basis of contemporary efforts to discover a grand unified theory to explain all the laws of physics. Nobel Laureate Leon M. Lederman and physicist Christopher T. Hill explain the supremely elegant concept of symmetry and all its profound ramifications to life on Earth and the universe at large in this eloquent, accessible popular science book. They not only clearly describe concepts normally reserved only for physicists and mathematicians, but they also instill an appreciation for the profound beauty of the universe’s inherent design. Central to the story of symmetry is an obscure, unpretentious, but extremely gifted German mathematician named Emmy Noether. Though still little known to the world, she impressed no less a scientist than Albert Einstein, who praised her "penetrating mathematical thinking." In some of her earliest work she proved that the law of the conservation of energy was connected to the idea of symmetry and thus laid the mathematical groundwork for what may be the most important concept of modern physics. Lederman and Hill reveal concepts about the universe, based on Noether’s work, that are largely unknown to the public and have wide-reaching implications in connection with the Big Bang, Einstein’s theory of relativity, quantum mechanics, and many other areas of physics. Through ingenious analogies and illustrations, they bring these astounding notions to life. This book will open your eyes to a universe you never knew existed. From the Trade Paperback edition.
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Author: K. W. Stevens

Publisher: Princeton University Press

ISBN: 1400864461

Category: Science

Page: 268

View: 9091

There have been many demonstrations, particularly for magnetic impurity ions in crystals, that spin-Hamiltonians are able to account for a wide range of experimental results in terms of much smaller numbers of parameters. Yet they were originally derived from crystal field theory, which contains a logical flaw; electrons on the magnetic ions are distinguished from those on the ligands. Thus there is a challenge: to replace crystal field theory with one of equal or greater predictive power that is based on a surer footing. The theory developed in this book begins with a generic Hamiltonian, one that is common to most molecular and solid state problems and that does not violate the symmetry requirements imposed on electrons and nuclei. Using a version of degenerate perturbation theory due to Bloch and the introduction of Wannier functions, projection operators, and unitary transformations, Stevens shows that it is possible to replace crystal field theory as a basis for the spin-Hamiltonians of single magnetic ions and pairs and lattices of magnetic ions, even when the nuclei have vibrational motion. The power of the method is further demonstrated by showing that it can be extended to include lattice vibration and conduction by electron hopping such as probably occurs in high-Tc superconductors. Thus Stevens shows how an apparently successful ad hoc method of the past can be replaced by a much more soundly based one that not only incorporates all the previous successes but appears to open the way to extensions far outside the scope of the previously available methods. So far only some of these have been explored. The book should therefore be of great interest to all physicists and chemists concerned with understanding the special properties of molecules and solids that are imposed by the presence of magnetic ions. Originally published in 1997. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
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The Artful Mathematics of Wallpaper Patterns

Author: Frank A. Farris

Publisher: Princeton University Press

ISBN: 1400865670

Category: Art

Page: 248

View: 9034

This lavishly illustrated book provides a hands-on, step-by-step introduction to the intriguing mathematics of symmetry. Instead of breaking up patterns into blocks—a sort of potato-stamp method—Frank Farris offers a completely new waveform approach that enables you to create an endless variety of rosettes, friezes, and wallpaper patterns: dazzling art images where the beauty of nature meets the precision of mathematics. Featuring more than 100 stunning color illustrations and requiring only a modest background in math, Creating Symmetry begins by addressing the enigma of a simple curve, whose curious symmetry seems unexplained by its formula. Farris describes how complex numbers unlock the mystery, and how they lead to the next steps on an engaging path to constructing waveforms. He explains how to devise waveforms for each of the 17 possible wallpaper types, and then guides you through a host of other fascinating topics in symmetry, such as color-reversing patterns, three-color patterns, polyhedral symmetry, and hyperbolic symmetry. Along the way, Farris demonstrates how to marry waveforms with photographic images to construct beautiful symmetry patterns as he gradually familiarizes you with more advanced mathematics, including group theory, functional analysis, and partial differential equations. As you progress through the book, you'll learn how to create breathtaking art images of your own. Fun, accessible, and challenging, Creating Symmetry features numerous examples and exercises throughout, as well as engaging discussions of the history behind the mathematics presented in the book.
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Author: B. H. Bransden,R. G. Moorhouse

Publisher: Princeton University Press

ISBN: 1400867444

Category: Technology & Engineering

Page: 550

View: 1815

Synthesizing the theoretical and experimental advances in pion-nucleon interactions over approximately the last twelve years, the authors offer here a timely account of the hadronic interactions of pions and nucleons and of the structure of nucleons. Because of the hadronic SU3 symmetry, the book also treats the structure of baryons in general, and so contains much material external to the specific field of pion-nucleon interactions. Thus the book's subject can be stated as the hadronic structure of baryons as illustrated particularly by pion-nucleon interaction. Following an introductory discussion of isotopic spin, the authors proceed to chapters that treat low energy pion scattering by nucleons and the photoproduction of pions; forward and fixed momentum transfer dispersion relations; analytic properties of scattering amplitudes; formation of nucleon resonances; symmetries and classification of particles and resonances; current algebra, sum rules, and superconvergence relations; scattering at higher energies; pion-nucleon dynamics; pion-nucleon inelastic scattering; and the form factors of the nucleon and the pion. Each chapter is followed by abundant references to the original literature. The level of the writing is suitable for students at the graduate level, and the presentation is even and self-contained. On balance, the authors have prepared a useful consolidation and review of this difficult and changing area of investigation. Originally published in 1973. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
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Author: Geerat J. Vermeij

Publisher: Princeton University Press

ISBN: 9780691001678

Category: Nature

Page: 207

View: 7998

Geerat Vermeij wrote this "celebration of shells" to share his enthusiasm for these supremely elegant creations and what they can teach us about nature. Most other popular books on shells emphasize the identification of species, but Vermeij uses shells as a way to explore major ideas in biology. How are shells built? How do they work? How did they evolve? With these questions in mind, the author lucidly - and charmingly - demonstrates how shells give us insights into the lives of animals in our own day as well as in the distant geological past. As snails, clams, and other molluscs enlarge their shells, they inscribe a detailed record of the everyday events and unusual circumstances that mark their lives. Moreover, the fossil record that chronicles the history of life is replete with shells of extinct species. Vermeij draws on comparisons of shells from different parts of the world and from successive geological periods to argue that predators have played a decisive role in the evolution of shells. Architectural specialization, he argues, is dictated by the risks, rewards, costs, and benefits imposed by predators and competitors on shell-builders living in a dangerous world. This book will be of interest both to amateur shell collectors and to scholars, and its lively review of evolutionary history should prove especially appealing to a general audience.
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Author: D.L. Johnson

Publisher: Springer Science & Business Media

ISBN: 1447102436

Category: Mathematics

Page: 198

View: 9271

" ... many eminent scholars, endowed with great geometric talent, make a point of never disclosing the simple and direct ideas that guided them, subordinating their elegant results to abstract general theories which often have no application outside the particular case in question. Geometry was becoming a study of algebraic, differential or partial differential equations, thus losing all the charm that comes from its being an art." H. Lebesgue, Ler;ons sur les Constructions Geometriques, Gauthier Villars, Paris, 1949. This book is based on lecture courses given to final-year students at the Uni versity of Nottingham and to M.Sc. students at the University of the West Indies in an attempt to reverse the process of expurgation of the geometry component from the mathematics curricula of universities. This erosion is in sharp contrast to the situation in research mathematics, where the ideas and methods of geometry enjoy ever-increasing influence and importance. In the other direction, more modern ideas have made a forceful and beneficial impact on the geometry of the ancients in many areas. Thus trigonometry has vastly clarified our concept of angle, calculus has revolutionised the study of plane curves, and group theory has become the language of symmetry.
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Author: Steven S. Gubser

Publisher: Princeton University Press

ISBN: 9781400834433

Category: Science

Page: 184

View: 6778

The Little Book of String Theory offers a short, accessible, and entertaining introduction to one of the most talked-about areas of physics today. String theory has been called the "theory of everything." It seeks to describe all the fundamental forces of nature. It encompasses gravity and quantum mechanics in one unifying theory. But it is unproven and fraught with controversy. After reading this book, you'll be able to draw your own conclusions about string theory. Steve Gubser begins by explaining Einstein's famous equation E = mc2 , quantum mechanics, and black holes. He then gives readers a crash course in string theory and the core ideas behind it. In plain English and with a minimum of mathematics, Gubser covers strings, branes, string dualities, extra dimensions, curved spacetime, quantum fluctuations, symmetry, and supersymmetry. He describes efforts to link string theory to experimental physics and uses analogies that nonscientists can understand. How does Chopin's Fantasie-Impromptu relate to quantum mechanics? What would it be like to fall into a black hole? Why is dancing a waltz similar to contemplating a string duality? Find out in the pages of this book. The Little Book of String Theory is the essential, most up-to-date beginner's guide to this elegant, multidimensional field of physics.
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A Critical Examination of the Foundation of Analysis

Author: Hermann Weyl

Publisher: Courier Corporation

ISBN: 0486679829

Category: Mathematics

Page: 130

View: 7731

Concise classic by great mathematician and physicist deals with logic and mathematics of set and function, concept of number and the continuum. Bibliography. Originally published 1918.
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Author: A. Zee

Publisher: Princeton University Press

ISBN: 1400881188

Category: Science

Page: 632

View: 2065

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)
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How It Really Works and Why It Matters

Author: Jeremy J. Baumberg

Publisher: Princeton University Press

ISBN: 1400889308

Category: Science

Page: 248

View: 806

A revealing and provocative look at the current state of global science We take the advance of science as given. But how does science really work? Is it truly as healthy as we tend to think? How does the system itself shape what scientists do? The Secret Life of Science takes a clear-eyed and provocative look at the current state of global science, shedding light on a cutthroat and tightly tensioned enterprise that even scientists themselves often don't fully understand. The Secret Life of Science is a dispatch from the front lines of modern science. It paints a startling picture of a complex scientific ecosystem that has become the most competitive free-market environment on the planet. It reveals how big this ecosystem really is, what motivates its participants, and who reaps the rewards. Are there too few scientists in the world or too many? Are some fields expanding at the expense of others? What science is shared or published, and who determines what the public gets to hear about? What is the future of science? Answering these and other questions, this controversial book explains why globalization is not necessarily good for science, nor is the continued growth in the number of scientists. It portrays a scientific community engaged in a race for limited resources that determines whether careers are lost or won, whose research visions become the mainstream, and whose vested interests end up in control. The Secret Life of Science explains why this hypercompetitive environment is stifling the diversity of research and the resiliency of science itself, and why new ideas are needed to ensure that the scientific enterprise remains healthy and vibrant.
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Author: Magdolna Hargittai,Istvan Hargittai

Publisher: Springer Science & Business Media

ISBN: 9781402056284

Category: Science

Page: 520

View: 1455

It is gratifying to launch the third edition of our book. Its coming to life testi?es about the task it has ful?lled in the service of the com- nity of chemical research and learning. As we noted in the Prefaces to the ?rst and second editions, our book surveys chemistry from the point of view of symmetry. We present many examples from ch- istry as well as from other ?elds to emphasize the unifying nature of the symmetry concept. Our aim has been to provide aesthetic pl- sure in addition to learning experience. In our ?rst Preface we paid tribute to two books in particular from which we learned a great deal; they have in?uenced signi?cantly our approach to the subject matter of our book. They are Weyl’s classic, Symmetry, and Shubnikov and Koptsik’s Symmetry in Science and Art. The structure of our book has not changed. Following the Int- duction (Chapter 1), Chapter 2 presents the simplest symmetries using chemical and non-chemical examples. Molecular geometry is discussed in Chapter 3. The next four chapters present gro- theoretical methods (Chapter 4) and, based on them, discussions of molecular vibrations (Chapter 5), electronic structures (Chapter 6), and chemical reactions (Chapter 7). For the last two chapters we return to a qualitative treatment and introduce space-group sym- tries (Chapter 8), concluding with crystal structures (Chapter 9). For the third edition we have further revised and streamlined our text and renewed the illustrative material.
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Selected Writings on Philosophy, Mathematics, and Physics

Author: Hermann Weyl

Publisher: Princeton University Press

ISBN: 9781400833320

Category: Mathematics

Page: 272

View: 1486

Hermann Weyl (1885-1955) was one of the twentieth century's most important mathematicians, as well as a seminal figure in the development of quantum physics and general relativity. He was also an eloquent writer with a lifelong interest in the philosophical implications of the startling new scientific developments with which he was so involved. Mind and Nature is a collection of Weyl's most important general writings on philosophy, mathematics, and physics, including pieces that have never before been published in any language or translated into English, or that have long been out of print. Complete with Peter Pesic's introduction, notes, and bibliography, these writings reveal an unjustly neglected dimension of a complex and fascinating thinker. In addition, the book includes more than twenty photographs of Weyl and his family and colleagues, many of which are previously unpublished. Included here are Weyl's exposition of his important synthesis of electromagnetism and gravitation, which Einstein at first hailed as "a first-class stroke of genius"; two little-known letters by Weyl and Einstein from 1922 that give their contrasting views on the philosophical implications of modern physics; and an essay on time that contains Weyl's argument that the past is never completed and the present is not a point. Also included are two book-length series of lectures, The Open World (1932) and Mind and Nature (1934), each a masterly exposition of Weyl's views on a range of topics from modern physics and mathematics. Finally, four retrospective essays from Weyl's last decade give his final thoughts on the interrelations among mathematics, philosophy, and physics, intertwined with reflections on the course of his rich life.
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Author: Lochlainn O'Raifeartaigh

Publisher: Princeton University Press

ISBN: 9780691029771

Category: Science

Page: 249

View: 6573

During the course of this century, gauge invariance has slowly emerged from being an incidental symmetry of electromagnetism to being a fundamental geometrical principle underlying the four known fundamental physical interactions. The development has been in two stages. In the first stage (1916-1956) the geometrical significance of gauge-invariance gradually came to be appreciated and the original abelian gauge-invariance of electromagnetism was generalized to non-abelian gauge invariance. In the second stage (1960-1975) it was found that, contrary to first appearances, the non-abelian gauge-theories provided exactly the framework that was needed to describe the nuclear interactions (both weak and strong) and thus provided a universal framework for describing all known fundamental interactions. In this work, Lochlainn O'Raifeartaigh describes the former phase. O'Raifeartaigh first illustrates how gravitational theory and quantum mechanics played crucial roles in the reassessment of gauge theory as a geometric principle and as a framework for describing both electromagnetism and gravitation. He then describes how the abelian electromagnetic gauge-theory was generalized to its present non-abelian form. The development is illustrated by including a selection of relevant articles, many of them appearing here for the first time in English, notably by Weyl, Schrodinger, Klein, and London in the pre-war years, and by Pauli, Shaw, Yang-Mills, and Utiyama after the war. The articles illustrate that the reassessment of gauge-theory, due in a large measure to Weyl, constituted a major philosophical as well as technical advance.
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Second Edition

Author: A. Zee

Publisher: Princeton University Press

ISBN: 9781400835324

Category: Science

Page: 608

View: 3116

Since it was first published, Quantum Field Theory in a Nutshell has quickly established itself as the most accessible and comprehensive introduction to this profound and deeply fascinating area of theoretical physics. Now in this fully revised and expanded edition, A. Zee covers the latest advances while providing a solid conceptual foundation for students to build on, making this the most up-to-date and modern textbook on quantum field theory available. This expanded edition features several additional chapters, as well as an entirely new section describing recent developments in quantum field theory such as gravitational waves, the helicity spinor formalism, on-shell gluon scattering, recursion relations for amplitudes with complex momenta, and the hidden connection between Yang-Mills theory and Einstein gravity. Zee also provides added exercises, explanations, and examples, as well as detailed appendices, solutions to selected exercises, and suggestions for further reading. The most accessible and comprehensive introductory textbook available Features a fully revised, updated, and expanded text Covers the latest exciting advances in the field Includes new exercises Offers a one-of-a-kind resource for students and researchers Leading universities that have adopted this book include: Arizona State University Boston University Brandeis University Brown University California Institute of Technology Carnegie Mellon College of William & Mary Cornell Harvard University Massachusetts Institute of Technology Northwestern University Ohio State University Princeton University Purdue University - Main Campus Rensselaer Polytechnic Institute Rutgers University - New Brunswick Stanford University University of California - Berkeley University of Central Florida University of Chicago University of Michigan University of Montreal University of Notre Dame Vanderbilt University Virginia Tech University
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