[PDF] Symmetry Broken Symmetry And Topology In Modern Physics eBook

Author : Mike Guidry
Publisher : Cambridge University Press
Page : 666 pages
File Size : 20,43 MB
Release : 2022-03-31
Category : Science
ISBN : 1009008420

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Written for use in teaching and for self-study, this book provides a comprehensive and pedagogical introduction to groups, algebras, geometry, and topology. It assimilates modern applications of these concepts, assuming only an advanced undergraduate preparation in physics. It provides a balanced view of group theory, Lie algebras, and topological concepts, while emphasizing a broad range of modern applications such as Lorentz and Poincaré invariance, coherent states, quantum phase transitions, the quantum Hall effect, topological matter, and Chern numbers, among many others. An example based approach is adopted from the outset, and the book includes worked examples and informational boxes to illustrate and expand on key concepts. 344 homework problems are included, with full solutions available to instructors, and a subset of 172 of these problems have full solutions available to students.

Author : Mike Guidry
Publisher : Cambridge University Press
Page : 665 pages
File Size : 11,60 MB
Release : 2022-03-31
Category : Mathematics
ISBN : 1316518612

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A pedagogical introduction to the modern applications of groups, algebras, and topology for undergraduate and graduate students in physics.

Author : Henryk Arodz
Publisher : Springer Science & Business Media
Page : 407 pages
File Size : 41,73 MB
Release : 2012-12-06
Category : Science
ISBN : 9400710291

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The conceptofspontaneous symmetry breaking plays a fundamental role in contemporary physics. It is essential for the description of degenerate ground states, massless modes, and topological defects. Examples are abundant in condensed matter physics, atomic and particle physics, as well as in astro physics and cosmology. In fact, spontaneous symmetry breaking can be re garded as a cornerstone ofa whole branch ofphysics which intersects the above mentioned traditionally distinct fields. In the year 2000 the European Science Foundation (ESF) started the Pro gramme "Cosmology in the Laboratory" (COSLAB), with the goal to search for and to develop analogies betweencondensed matterphysics, particle physics, and cosmology. Not surprisingly, spontaneous symmetry breaking is among the most useful notions in that endeavour. It has been decided that in the sec ond year of the Programme a School should be held in order to work out and deliver to a wide audience of students synthetic overviews of achievements and of current research topics of COSLAB. This idea has been supported by the Scientific and Environmental Affairs Division of NATO by including the School in the renowned series of its Advanced Study Institutes. The School, entitled" Patterns of Symmetry Breaking", was held in Cracow during 16-28 September 2002. It gathered 17 lecturers and about 60 students. The present volume contains notes ofmost of the lectures from that School. We hope that of the physics of spon it will convey to the reader the breadth and the beauty taneous symmetry breaking.

Author : Franco Strocchi
Publisher : Springer Science & Business Media
Page : 220 pages
File Size : 28,90 MB
Release : 2005-02-21
Category : Science
ISBN : 9783540213185

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The intriguing mechanism of spontaneous symmetry breaking is a powerful innovative idea at the basis of most of the recent developments in theoretical physics, from statistical mechanics to many-body theory to elementary particles theory; for infinitely extended systems a symmetric Hamiltonian can account for non symmetric behaviours, giving rise to non symmetric realizations of a physical system. In the first part of this book, devoted to classical field theory, such a mechanism is explained in terms of the occurrence of disjoint sectors and their stability properties and of an improved version of the Noether theorem. For infinitely extended quantum systems, discussed in the second part, the mechanism is related to the occurrence of disjoint pure phases and characterized by a symmetry breaking order parameter, for which non perturbative criteria are discussed, following Wightman, and contrasted with the standard Goldstone perturbative strategy. The Goldstone theorem is discussed with a critical look at the hypotheses that emphasizes the crucial role of the dynamical delocalization induced by the interaction range. The Higgs mechanism in local gauges is explained in terms of the Gauss law constraint on the physical states. The mathematical details are kept to the minimum required to make the book accessible to students with basic knowledge of Hilbert space structures. Much of the material has not appeared in other textbooks.

Author : Franco Strocchi
Publisher : Springer
Page : 212 pages
File Size : 22,38 MB
Release : 2007-10-31
Category : Science
ISBN : 3540735933

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The new edition of this well received primer on rigorous aspects of symmetry breaking presents a more detailed and thorough discussion of the mechanism of symmetry breaking in classical field theory in relation with the Noether theorem. Moreover, the link between symmetry breaking without massless Goldstone bosons in Coulomb systems and in gauge theories is made more explicit. A subject index has been added and a number of misprints have been corrected.

Author : Michael I. Monastyrsky
Publisher : Springer Science & Business Media
Page : 263 pages
File Size : 32,53 MB
Release : 2006-02-04
Category : Science
ISBN : 3540312641

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This book reports new results in condensed matter physics for which topological methods and ideas are important. It considers, on the one hand, recently discovered systems such as carbon nanocrystals and, on the other hand, new topological methods used to describe more traditional systems such as the Fermi surfaces of normal metals, liquid crystals and quasicrystals. The authors of the book are renowned specialists in their fields and present the results of ongoing research, some of it obtained only very recently and not yet published in monograph form.

Author : Stephanie Frank Singer
Publisher : Springer Science & Business Media
Page : 612 pages
File Size : 34,86 MB
Release : 2001-03-01
Category : Mathematics
ISBN : 9780817641450

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"And what is the use," thought Alice, "of a book without pictures or conversations in it?" -Lewis Carroll This book is written for modem undergraduate students - not the ideal stu dents that mathematics professors wish for (and who occasionally grace our campuses), but the students like many the author has taught: talented but ap preciating review and reinforcement of past course work; willing to work hard, but demanding context and motivation for the mathematics they are learning. To suit this audience, the author eschews density of topics and efficiency of presentation in favor of a gentler tone, a coherent story, digressions on mathe maticians, physicists and their notations, simple examples worked out in detail, and reinforcement of the basics. Dense and efficient texts play a crucial role in the education of budding (and budded) mathematicians and physicists. This book does not presume to improve on the classics in that genre. Rather, it aims to provide those classics with a large new generation of appreciative readers. This text introduces some basic constructs of modern symplectic geometry in the context of an old celestial mechanics problem, the two-body problem. We present the derivation of Kepler's laws of planetary motion from Newton's laws of gravitation, first in the style of an undergraduate physics course, and x Preface then again in the language of symplectic geometry. No previous exposure to symplectic geometry is required: we introduce and illustrate all necessary con structs.

Author : Yuriy M. Bunkov
Publisher : Springer Science & Business Media
Page : 388 pages
File Size : 28,76 MB
Release : 2012-12-06
Category : Science
ISBN : 9401141061

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Topological defects formed at symmetry-breaking phase transitions play an important role in many different fields of physics. They appear in many condensed-matter systems at low temperature; examples include vortices in superfluid helium-4, a rich variety of defects in helium-3, quantized mag netic flux tubes in type-II superconductors, and disclination lines and other defects in liquid crystals. In cosmology, unified gauge theories of particle interactions suggest a sequence of phase transitions in the very early uni verse some of which may lead to defect formation. In astrophysics, defects play an important role in the dynamics of neutron stars. In 1997 the European Science Foundation started the scientific network "Topological defects" headed by Tom Kibble. This network has provided us with a unique opportunity of establishing a collaboration between the representatives of these very different branches of modern physics. The NATO-ASI (Advanced Study Institute), held in Les Houches in February 1999 thanks to the support of the Scientific Division of NATO, the European Science Foundation and the CNRS, represents a key event of this ESF network. It brought together participants from widely different fields, with diverse expertise and vocabulary, fostering the exchange of ideas. The lectures given by particle physicists, cosmologists and condensed matter physicists are the result of the fruitful collaborations established since 1997 between groups in several European countries and in the U.S.A.

Author : Sidney Coleman
Publisher : Cambridge University Press
Page : 424 pages
File Size : 23,14 MB
Release : 1988-02-18
Category : Science
ISBN : 1139810960

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For almost two decades, Sidney Coleman has been giving review lectures on frontier topics in theoretical high-energy physics at the International School of Subnuclear Physics held each year at Erice, Sicily. This volume is a collection of some of the best of these lectures. To this day they have few rivals for clarity of exposition and depth of insight. Although very popular when first published, many of the lectures have been difficult to obtain recently. Graduate students and professionals in high-energy physics will welcome this collection by a master of the field.