Supersymmetry And Noncommutative Geometry

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Supersymmetry and Noncommutative Geometry

Author : Wim Beenakker
Publisher : Springer
ISBN 13 : 3319247980
Total Pages : 137 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis Supersymmetry and Noncommutative Geometry by : Wim Beenakker

Download or read book Supersymmetry and Noncommutative Geometry written by Wim Beenakker and published by Springer. This book was released on 2015-10-22 with total page 137 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this work the question whether noncommutative geometry allows for supersymmetric theories is addressed. Noncommutative geometry has seen remarkable applications in high energy physics, viz. the geometrical interpretation of the Standard Model, however such a question has not been answered in a conclusive way so far.The book starts with a systematic analysis of the possibilities for so-called almost-commutative geometries on a 4-dimensional, flat background to exhibit not only a particle content that is eligible for supersymmetry, but also have a supersymmetric action. An approach is proposed in which the basic `building blocks' of potentially supersymmetric theories and the demands for their action to be supersymmetric are identified. It is then described how a novel kind of soft supersymmetry breaking Lagrangian arises naturally from the spectral action. Finally, the above formalism is applied to explore the existence of a noncommutative version of the minimal supersymmetric Standard Model.This book is intended for mathematical/theoretical physicists with an interest in the applications of noncommutative geometry to supersymmetric field theories.

Concise Encyclopedia of Supersymmetry

Author : Steven Duplij
Publisher : Springer Science & Business Media
ISBN 13 : 1402013388
Total Pages : 516 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Concise Encyclopedia of Supersymmetry by : Steven Duplij

Download or read book Concise Encyclopedia of Supersymmetry written by Steven Duplij and published by Springer Science & Business Media. This book was released on 2005-11-07 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is the first full-size Encyclopedia which simultaneously covers such well-established and modern subjects as quantum field theory, supersymmetry, supergravity, M-theory, black holes and quantum gravity, noncommutative geometry, representation theory, categories and quantum groups, and their generalizations. The extraordinary historical part "the SUSY story," more than 700 authored articles from more than 250 high-level experts (including Nobel Prize Winner Gerard 't Hooft), a detailed (50 pages) Subject/Article three level index and an Author index, make the SUSY Encyclopedia an outstanding and indispensable book on the desk of researchers, experts, Ph.D. students, specialists and professionals in modern methods of theoretical and mathematical physics.

Noncommutative Structures in Mathematics and Physics

Author : S. Duplij
Publisher : Springer Science & Business Media
ISBN 13 : 9401008361
Total Pages : 472 pages
Book Rating : 4.4/5 (1 download)

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Book Synopsis Noncommutative Structures in Mathematics and Physics by : S. Duplij

Download or read book Noncommutative Structures in Mathematics and Physics written by S. Duplij and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: A presentation of outstanding achievements and ideas, of both eastern and western scientists, both mathematicians and physicists. Their presentations of recent work on quantum field theory, supergravity, M-theory, black holes and quantum gravity, together with research into noncommutative geometry, Hopf algebras, representation theory, categories and quantum groups, take the reader to the forefront of the latest developments. Other topics covered include supergravity and branes, supersymmetric quantum mechanics and superparticles, (super) black holes, superalgebra representations, and SUSY GUT phenomenology. Essential reading for workers in the modern methods of theoretical and mathematical physics.

Noncommutative Geometry and Particle Physics

Author : Walter D. van Suijlekom
Publisher : Springer
ISBN 13 : 9401791627
Total Pages : 246 pages
Book Rating : 4.4/5 (17 download)

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Book Synopsis Noncommutative Geometry and Particle Physics by : Walter D. van Suijlekom

Download or read book Noncommutative Geometry and Particle Physics written by Walter D. van Suijlekom and published by Springer. This book was released on 2014-07-21 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to noncommutative geometry and presents a number of its recent applications to particle physics. It is intended for graduate students in mathematics/theoretical physics who are new to the field of noncommutative geometry, as well as for researchers in mathematics/theoretical physics with an interest in the physical applications of noncommutative geometry. In the first part, we introduce the main concepts and techniques by studying finite noncommutative spaces, providing a “light” approach to noncommutative geometry. We then proceed with the general framework by defining and analyzing noncommutative spin manifolds and deriving some main results on them, such as the local index formula. In the second part, we show how noncommutative spin manifolds naturally give rise to gauge theories, applying this principle to specific examples. We subsequently geometrically derive abelian and non-abelian Yang-Mills gauge theories, and eventually the full Standard Model of particle physics, and conclude by explaining how noncommutative geometry might indicate how to proceed beyond the Standard Model.

An Introduction to Two-Dimensional Quantum Field Theory with (0,2) Supersymmetry

Author : Ilarion V. Melnikov
Publisher : Springer
ISBN 13 : 3030050858
Total Pages : 482 pages
Book Rating : 4.0/5 (3 download)

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Book Synopsis An Introduction to Two-Dimensional Quantum Field Theory with (0,2) Supersymmetry by : Ilarion V. Melnikov

Download or read book An Introduction to Two-Dimensional Quantum Field Theory with (0,2) Supersymmetry written by Ilarion V. Melnikov and published by Springer. This book was released on 2019-02-11 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces two-dimensional supersymmetric field theories with emphasis on both linear and non-linear sigma models. Complex differential geometry, in connection with supersymmetry, has played a key role in most developments of the last thirty years in quantum field theory and string theory. Both structures introduce a great deal of rigidity compared to the more general categories of non-supersymmetric theories and real differential geometry, allowing for many general conceptual results and detailed quantitative predictions. Two-dimensional (0,2) supersymmetric quantum field theories provide a natural arena for the fruitful interplay between geometry and quantum field theory. These theories play an important role in string theory and provide generalizations, still to be explored fully, of rich structures such as mirror symmetry. They also have applications to non-perturbative four-dimensional physics, for instance as descriptions of surface defects or low energy dynamics of solitonic strings in four-dimensional supersymmetric theories. The purpose of these lecture notes is to acquaint the reader with these fascinating theories, assuming a background in conformal theory, quantum field theory and differential geometry at the beginning graduate level. In order to investigate the profound relations between structures from complex geometry and field theory the text begins with a thorough examination of the basic structures of (0,2) quantum field theory and conformal field theory. Next, a simple class of Lagrangian theories, the (0,2) Landau-Ginzburg models, are discussed, together with the resulting renormalization group flows, dynamics, and symmetries. After a thorough introduction and examination of (0,2) non-linear sigma models, the text introduces linear sigma models that, in particular, provide a unified treatment of non-linear sigma models and Landau-Ginzburg theories. Many exercises, along with discussions of relevant mathematical notions and important open problems in the field, are included in the text.

Advances in Noncommutative Geometry

Author : Ali Chamseddine
Publisher : Springer Nature
ISBN 13 : 3030295974
Total Pages : 753 pages
Book Rating : 4.0/5 (32 download)

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Book Synopsis Advances in Noncommutative Geometry by : Ali Chamseddine

Download or read book Advances in Noncommutative Geometry written by Ali Chamseddine and published by Springer Nature. This book was released on 2020-01-13 with total page 753 pages. Available in PDF, EPUB and Kindle. Book excerpt: This authoritative volume in honor of Alain Connes, the foremost architect of Noncommutative Geometry, presents the state-of-the art in the subject. The book features an amalgam of invited survey and research papers that will no doubt be accessed, read, and referred to, for several decades to come. The pertinence and potency of new concepts and methods are concretely illustrated in each contribution. Much of the content is a direct outgrowth of the Noncommutative Geometry conference, held March 23–April 7, 2017, in Shanghai, China. The conference covered the latest research and future areas of potential exploration surrounding topology and physics, number theory, as well as index theory and its ramifications in geometry.

Lectures on Fuzzy and Fuzzy SUSY Physics

Author : A. P. Balachandran
Publisher : World Scientific
ISBN 13 : 9812707468
Total Pages : 196 pages
Book Rating : 4.8/5 (127 download)

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Book Synopsis Lectures on Fuzzy and Fuzzy SUSY Physics by : A. P. Balachandran

Download or read book Lectures on Fuzzy and Fuzzy SUSY Physics written by A. P. Balachandran and published by World Scientific. This book was released on 2007 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: Noncommutative geometry provides a powerful tool for regularizing quantum field theories in the form of fuzzy physics. Fuzzy physics maintains symmetries, has no fermion-doubling problem and represents topological features efficiently. These lecture notes provide a comprehensive introduction to the field. Starting with the construction of fuzzy spaces, using the concrete examples of the fuzzy sphere and fuzzy complex projective spaces, the book moves on to discuss the technology of star products on noncommutative R2d and on the fuzzy sphere. Scalar, spinor and gauge field theories as well as extended objects such as monopoles and nonlinear sigma modes are treated in considerable detail. A detailed treatment of the regularization of supersymmetry is given using the techniques of fuzzy physics.

Supersymmetry in Mathematics and Physics

Author : Sergio Ferrara
Publisher : Springer Science & Business Media
ISBN 13 : 3642217435
Total Pages : 279 pages
Book Rating : 4.6/5 (422 download)

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Book Synopsis Supersymmetry in Mathematics and Physics by : Sergio Ferrara

Download or read book Supersymmetry in Mathematics and Physics written by Sergio Ferrara and published by Springer Science & Business Media. This book was released on 2011-08-28 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: Supersymmetry was created by the physicists in the 1970's to give a unified treatment of fermions and bosons, the basic constituents of matter. Since then its mathematical structure has been recognized as that of a new development in geometry, and mathematicians have busied themselves with exploring this aspect. This volume collects recent advances in this field, both from a physical and a mathematical point of view, with an accent on a rigorous treatment of the various questions raised.

Noncommutative Geometry and Physics

Author :
Publisher :
ISBN 13 : 9814479411
Total Pages : pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Noncommutative Geometry and Physics by :

Download or read book Noncommutative Geometry and Physics written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Quantum Field Theory, Supersymmetry, and Enumerative Geometry

Author : Daniel S. Freed
Publisher : American Mathematical Soc.
ISBN 13 : 0821834312
Total Pages : 297 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Quantum Field Theory, Supersymmetry, and Enumerative Geometry by : Daniel S. Freed

Download or read book Quantum Field Theory, Supersymmetry, and Enumerative Geometry written by Daniel S. Freed and published by American Mathematical Soc.. This book was released on 2006 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: Each summer the IAS/Park City Mathematics Institute Graduate Summer School gathers some of the best researchers and educators in a particular field to present diverse sets of lectures. This volume presents three weeks of lectures given at the Summer School on Quantum Field Theory, Supersymmetry, and Enumerative Geometry, three very active research areas in mathematics and theoretical physics. With this volume, the Park City Mathematics Institute returns to the general topic of the first institute: the interplay between quantum field theory and mathematics. Two major themes at this institute were supersymmetry and algebraic geometry, particularly enumerative geometry. The volume contains two lecture series on methods of enumerative geometry that have their roots in QFT. The first series covers the Schubert calculus and quantum cohomology. The second discusses methods from algebraic geometry for computing Gromov-Witten invariants. There are also three sets of lectures of a more introductory nature: an overview of classical field theory and supersymmetry, an introduction to supermanifolds, and an introduction to general relativity. This volume is recommended for independent study and is suitable for graduate students and researchers interested in geometry and physics. Information for our distributors: Titles in this series are copublished with the Institute for Advanced Study/Park City Mathematics Institute. Members of the Mathematical Association of America (MAA) and the National Council of Teachers of Mathematics (NCTM) receive a 20% discount from list price.

Noncommutative Geometry and Physics 3

Author : Giuseppe Dito
Publisher : World Scientific
ISBN 13 : 981442501X
Total Pages : 537 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Noncommutative Geometry and Physics 3 by : Giuseppe Dito

Download or read book Noncommutative Geometry and Physics 3 written by Giuseppe Dito and published by World Scientific. This book was released on 2013 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: Noncommutative differential geometry has many actual and potential applications to several domains in physics ranging from solid state to quantization of gravity. The strategy is to formulate usual differential geometry in a somewhat unusual manner, using in particular operator algebras and related concepts, so as to be able to plug in noncommutativity in a natural way. Algebraic tools such as K-theory and cyclic cohomology and homology play an important role in this field.

Noncommutative Geometry and Physics 2005

Author :
Publisher : World Scientific
ISBN 13 : 9812779647
Total Pages : 333 pages
Book Rating : 4.8/5 (127 download)

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Book Synopsis Noncommutative Geometry and Physics 2005 by :

Download or read book Noncommutative Geometry and Physics 2005 written by and published by World Scientific. This book was released on 2007 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive overview of the authors' pioneering contributions to nonlinear set-valued analysis by topological methods. The coverage includes fixed point theory, degree theory, the KKM principle, variational inequality theory, the Nash equilibrium point in mathematical economics, the Pareto optimum in optimization, and applications to best approximation theory, partial equations and boundary value problems. Self-contained and unified in presentation, the book considers the existence of equilibrium points of abstract economics in topological vector spaces from the viewpoint of Ky Fan minimax inequalities. It also provides the latest developments in KKM theory and degree theory for nonlinear set-valued mappings.

Special Metrics and Supersymmetry

Author : Luis Carlos de Andrés
Publisher : American Institute of Physics
ISBN 13 :
Total Pages : 220 pages
Book Rating : 4.:/5 (318 download)

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Book Synopsis Special Metrics and Supersymmetry by : Luis Carlos de Andrés

Download or read book Special Metrics and Supersymmetry written by Luis Carlos de Andrés and published by American Institute of Physics. This book was released on 2009-02-25 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: All papers have been peer-reviewed. This volume includes the contributions to the International Workshop on Geometry and Physics: Special Metrics and Supersymmetry, held at the University of the Basque Country, Bilbao (Spain), from May 29 to 31, 2008. The topics covered by the volume deal with leading aspects of algebraic and differential geometry with special emphasis to their potential applications in supersymmetry and string theories. The areas covered by the proceedings are algebraic geometry, differential geometry and mathematical physics. In greater detail, they cover outstanding topics such as homological mirror symmetry, generalized Hodge theory, coassociative submanifolds, special geometric structures, geometric structures, Killing spinors, torsion geometry, string theory, supersymmetry and T-duality, among others.

Noncommutative Spacetimes

Author : Paolo Aschieri
Publisher : Springer Science & Business Media
ISBN 13 : 3540897925
Total Pages : 205 pages
Book Rating : 4.5/5 (48 download)

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Book Synopsis Noncommutative Spacetimes by : Paolo Aschieri

Download or read book Noncommutative Spacetimes written by Paolo Aschieri and published by Springer Science & Business Media. This book was released on 2009-07-14 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: There are many approaches to noncommutative geometry and to its use in physics. This volume addresses the subject by combining the deformation quantization approach, based on the notion of star-product, and the deformed quantum symmetries methods, based on the theory of quantum groups. The aim of this work is to give an introduction to this topic and to prepare the reader to enter the research field quickly. The order of the chapters is "physics first": the mathematics follows from the physical motivations (e.g. gauge field theories) in order to strengthen the physical intuition. The new mathematical tools, in turn, are used to explore further physical insights. A last chapter has been added to briefly trace Julius Wess' (1934-2007) seminal work in the field.

Topics in Noncommutative Geometry

Author : I͡U. I. Manin
Publisher :
ISBN 13 : 9780691085883
Total Pages : 163 pages
Book Rating : 4.0/5 (858 download)

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Book Synopsis Topics in Noncommutative Geometry by : I͡U. I. Manin

Download or read book Topics in Noncommutative Geometry written by I͡U. I. Manin and published by . This book was released on 1991 with total page 163 pages. Available in PDF, EPUB and Kindle. Book excerpt: There is a well-known correspondence between the objects of algebra and geometry: a space gives rise to a function algebra; a vector bundle over the space corresponds to a projective module over this algebra; cohomology can be read off the de Rham complex; and so on. In this book Yuri Manin addresses a variety of instances in which the application of commutative algebra cannot be used to describe geometric objects, emphasizing the recent upsurge of activity in studying noncommutative rings as if they were function rings on "noncommutative spaces." Manin begins by summarizing and giving examples of some of the ideas that led to the new concepts of noncommutative geometry, such as Connes' noncommutative de Rham complex, supergeometry, and quantum groups. He then discusses supersymmetric algebraic curves that arose in connection with superstring theory; examines superhomogeneous spaces, their Schubert cells, and superanalogues of Weyl groups; and provides an introduction to quantum groups. This book is intended for mathematicians and physicists with some background in Lie groups and complex geometry. Originally published in 1991. 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 paperback editions preserve the original texts of these important books while presenting them in durable paperback 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.

Advances in Geometry and Lie Algebras from Supergravity

Author : Pietro Giuseppe Frè
Publisher : Springer
ISBN 13 : 3319744917
Total Pages : 556 pages
Book Rating : 4.3/5 (197 download)

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Book Synopsis Advances in Geometry and Lie Algebras from Supergravity by : Pietro Giuseppe Frè

Download or read book Advances in Geometry and Lie Algebras from Supergravity written by Pietro Giuseppe Frè and published by Springer. This book was released on 2018-02-24 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book aims to provide an overview of several topics in advanced differential geometry and Lie group theory, all of them stemming from mathematical problems in supersymmetric physical theories. It presents a mathematical illustration of the main development in geometry and symmetry theory that occurred under the fertilizing influence of supersymmetry/supergravity. The contents are mainly of mathematical nature, but each topic is introduced by historical information and enriched with motivations from high energy physics, which help the reader in getting a deeper comprehension of the subject.

An Introduction to Noncommutative Geometry

Author : Joseph C. Várilly
Publisher : European Mathematical Society
ISBN 13 : 9783037190241
Total Pages : 134 pages
Book Rating : 4.1/5 (92 download)

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Book Synopsis An Introduction to Noncommutative Geometry by : Joseph C. Várilly

Download or read book An Introduction to Noncommutative Geometry written by Joseph C. Várilly and published by European Mathematical Society. This book was released on 2006 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: Noncommutative geometry, inspired by quantum physics, describes singular spaces by their noncommutative coordinate algebras and metric structures by Dirac-like operators. Such metric geometries are described mathematically by Connes' theory of spectral triples. These lectures, delivered at an EMS Summer School on noncommutative geometry and its applications, provide an overview of spectral triples based on examples. This introduction is aimed at graduate students of both mathematics and theoretical physics. It deals with Dirac operators on spin manifolds, noncommutative tori, Moyal quantization and tangent groupoids, action functionals, and isospectral deformations. The structural framework is the concept of a noncommutative spin geometry; the conditions on spectral triples which determine this concept are developed in detail. The emphasis throughout is on gaining understanding by computing the details of specific examples. The book provides a middle ground between a comprehensive text and a narrowly focused research monograph. It is intended for self-study, enabling the reader to gain access to the essentials of noncommutative geometry. New features since the original course are an expanded bibliography and a survey of more recent examples and applications of spectral triples.