Continuous Symmetry

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Continuous Symmetry
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Author : William H. Barker
language : en
Publisher: American Mathematical Soc.
Release Date : 2007
Continuous Symmetry written by William H. Barker and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
The fundamental idea of geometry is that of symmetry. With that principle as the starting point, Barker and Howe begin an insightful and rewarding study of Euclidean geometry. The primary focus of the book is on transformations of the plane. The transformational point of view provides both a path for deeper understanding of traditional synthetic geometry and tools for providing proofs that spring from a consistent point of view. As a result, proofs become more comprehensible, as techniques can be used and reused in similar settings. The approach to the material is very concrete, with complete explanations of all the important ideas, including foundational background. The discussions of the nine-point circle and wallpaper groups are particular examples of how the strength of the transformational point of view and the care of the authors' exposition combine to give a remarkable presentation of topics in geometry. This text is for a one-semester undergraduate course on geometry. It is richly illustrated and contains hundreds of exercises.
Symmetry Breaking
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Author : Franco Strocchi
language : en
Publisher: Springer
Release Date : 2007-10-31
Symmetry Breaking written by Franco Strocchi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-10-31 with Science categories.
The main motivation for such lecture notes is the importance of the concept and mechanism of spontaneous symmetry breaking in modern theoretical physics and the relevance of a textbook exposition at the graduate student level beyond the oversimpli?ed (non-rigorous) treatments, often con?ned to speci?c models. One of the main points is to emphasize that the radical loss of symmetric behaviour requiresboth the existence of non-symmetric ground states and the in?nite extension of the system. The ?rst Part on SYMMETRY BREAKING IN CLASSICAL SYSTEMS is devoted to the mathematical understanding of spontaneous symmetry breaking on the basis of classical ?eld theory. The main points, which do not seem to appear in textbooks, are the following. i) ExistenceofdisjointHilbertspacesectors, stable under time e- lution in the set of solutions of the classical (non-linear) ?eld equations. Theyarethestrictanalogsofthedi?erentphasesofstatisticalmechanical systems and/or of the inequivalent representations of local ?eld algebras in quantum ?eld theory (QFT). As in QFT, such structures rely on the concepts of locality (or localization) and stability, (see Chap. 5), with emphasis on the physicalmotivations of the mathematicalconcepts; such structures have the physical meaning of disjoint physical worlds, disjoint phases etc. which can be associated to a given non-linear ?eld equation. The result of Theorem 5.2 may be regarded as a generalization of the criterium of stability to in?nite dimensional systems and it links such n stability to elliptic problems inR with non-trivial boundary conditions at in?nity (Appendix E).
Symmetry A Very Short Introduction
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Author : Ian Stewart
language : en
Publisher: OUP Oxford
Release Date : 2013-05-30
Symmetry A Very Short Introduction written by Ian Stewart and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-05-30 with Mathematics categories.
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.
Manifolds Of Symmetry
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Author : Pasquale De Marco
language : en
Publisher: Pasquale De Marco
Release Date :
Manifolds Of Symmetry written by Pasquale De Marco and has been published by Pasquale De Marco this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
In the realm of mathematics and physics, there exists an intricate tapestry of interconnected concepts that unveils the profound unity of the universe. Lie groups and manifolds stand as central players in this tapestry, revealing the harmonious interplay between symmetry, geometry, and the fundamental forces that govern our world. This book embarks on an enthralling journey through the fascinating world of Lie groups and manifolds, inviting readers to unravel their hidden beauty and unlock their transformative power. With engaging prose and accessible explanations, the book delves into the enigmatic nature of manifolds, unveiling their intricate structures and uncovering their hidden dimensions. Through the lens of Lie groups and manifolds, readers embark on a quest to comprehend the intricate workings of the universe. They witness the emergence of new mathematical structures, such as vector bundles and differential forms, which unveil hidden symmetries and unlock the secrets of geometry. The book masterfully weaves together abstract concepts with real-world applications, illuminating the patterns of nature, unraveling the mysteries of the cosmos, and providing a foundation for understanding the complexities of human behavior. Unveiling the interplay between Lie groups and manifolds, the book unveils the profound unity that underlies the diverse phenomena of the physical world. With each chapter, readers gain a deeper appreciation for the beauty and elegance of mathematics, and its transformative power in unraveling the mysteries of the universe. Written with clarity and precision, this book is an invaluable resource for students, researchers, and anyone seeking to explore the captivating world of Lie groups and manifolds. It provides a comprehensive introduction to these fundamental concepts, guiding readers through their rich history, intricate structures, and wide-ranging applications. This book is an invitation to embark on an intellectual adventure, where the boundaries of mathematics, physics, and the natural world dissolve, revealing the underlying unity and harmony of the universe. If you like this book, write a review!
Complex Symmetries
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Author : György Darvas
language : en
Publisher: Springer Nature
Release Date : 2022-01-01
Complex Symmetries written by György Darvas and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-01 with Mathematics categories.
This volume is a collection of essays on complex symmetries. It is curated, emphasizing the analysis of the symmetries, not the various phenomena that display those symmetries themselves. With this, the volume provides insight to nonspecialist readers into how individual simple symmetries constitute complex symmetry. The authors and the topics cover many different disciplines in various sciences and arts. Simple symmetries, such as reflection, rotation, translation, similitude, and a few other simple manifestations of the phenomenon, are all around, and we are aware of them in our everyday lives. However, there are myriads of complex symmetries (composed of a bulk of simple symmetries) as well. For example, the well-known helix represents the combination of translational and rotational symmetry. Nature produces a great variety of such complex symmetries. So do the arts. The contributions in this volume analyse selected examples (not limited to geometric symmetries). These include physical symmetries, functional (meaning not morphological) symmetries, such as symmetries in the construction of the genetic code, symmetries in human perception (e.g., in geometry education as well as in constructing physical theories), symmetries in fractal structures and structural morphology, including quasicrystal and fullerene structures in stable bindings and their applications in crystallography and architectural design, as well as color symmetries in the arts. The volume is rounded of with beautiful illustrations and presents a fascinating panorama of this interdisciplinary topic.
Symmetry Ornament And Modularity
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Author : Slavik V. Jablan
language : en
Publisher: World Scientific
Release Date : 2002
Symmetry Ornament And Modularity written by Slavik V. Jablan and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
This book discusses the origins of ornamental art -- illustrated by the oldest examples, dating mostly from the paleolithic and neolithic ages, and considered from the theory-of-symmetry point of view. Because of its multidisciplinary nature, it will interest a wide range of readers: mathematicians, artists, art historians, architects, psychologists, and anthropologists. The book represents the complete analysis of plane symmetry structures, so it can be used by artists as a guide to the creation of new symmetry patterns. Some parts of the contents (such as Chapter 4, about conformal symmetry, and Chapter 6, about modularity in art) give the reader an opportunity to develop computer programs for producing images illustrating the corresponding symmetry forms.
Quantum Symmetries
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Author : Thomas Creutzig
language : en
Publisher: American Mathematical Society
Release Date : 2025-03-19
Quantum Symmetries written by Thomas Creutzig and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-19 with Mathematics categories.
This volume contains the proceedings of the thematic program on ?Quantum symmetries: Tensor categories, topological quantum field theories, and vertex algebras? held from October 10?November 4, 2022, at the Centre de Recherches Math‚matiques, Montr‚al, Qu‚bec, Canada. Quantum symmetries is a rapidly expanding area in which tensor categories are applied to mathematical physics, in particular, to conformal and topological quantum field theories. These fields, in turn, connect to a huge variety of modern mathematics, including representation theory, vertex operator algebras, Hopf algebras, link and knot invariants, geometry, subfactors, combinatorics, and so much more. The thematic program on quantum symmetries featured advanced lecture courses and research seminars by international leaders of their respective fields. This proceedings volume is centered on the active research of the area, but also includes an in-depth survey of one of the main topics, $W$-algebras.
Symmetries In Physics
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Author : Katherine Brading
language : en
Publisher: Cambridge University Press
Release Date : 2003-12-04
Symmetries In Physics written by Katherine Brading and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-12-04 with Science categories.
This book brings together philosophical discussions of symmetry in physics, highlighting the main issues and controversies. It covers all the fundamental symmetries of modern physics, as well as discussing symmetry-breaking and general interpretational issues. For each topic, classic texts are followed by review articles and short commentaries.
Extreme States Of Matter In Strong Interaction Physics
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Author : Helmut Satz
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-03-17
Extreme States Of Matter In Strong Interaction Physics written by Helmut Satz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-03-17 with Science categories.
The thermodynamics of strongly interacting matter has become a profound and challenging area of modern physics, both in theory and in experiment. Statistical quantum chromodynamics, through analytical as well as numerical studies, provides the main theoretical tool, while in experiment, high-energy nuclear collisions are the key for extensive laboratory investigations. The field therefore straddles statistical, particle and nuclear physics, both conceptually and in the methods of investigation used. This course-tested primer addresses above all the many young scientists starting their scientific research in this field, providing them with a general, self-contained introduction that emphasizes in particular the basic concepts and ideas, with the aim of explaining why we do what we do. To achieve this goal, the present text concentrates mainly on equilibrium thermodynamics: first, the fundamental ideas of strong interaction thermodynamics are introduced and then the main concepts and methods used in the study of the physics of complex systems are summarized. Subsequently, simplified phenomenological pictures, leading to critical behavior in hadronic matter and to hadron-quark phase transitions are introduced, followed by elements of finite-temperature lattice QCD leading to the important results obtained in computer simulation studies of the lattice approach. Next, the relation of the resulting critical behavior to symmetry breaking/restoration in QCD is clarified before the text turns to the study of the QCD phase diagram. The presentation of bulk equilibrium thermodynamics is completed by studying the properties of the quark-gluon plasma as new state of strongly interacting matter. The final chapters of the book are devoted to more specific topics which arise when nuclear collisions are considered as a tool for the experimental study of QCD thermodynamics.
Symmetries In Fundamental Physics
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Author : Kurt Sundermeyer
language : en
Publisher: Springer
Release Date : 2014-07-23
Symmetries In Fundamental Physics written by Kurt Sundermeyer and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-23 with Science categories.
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.