Differential Geometry Through Supersymmetric Glasses

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Differential Geometry Through Supersymmetric Glasses

Author : Andrei Smilga
Publisher : World Scientific
ISBN 13 : 9811206791
Total Pages : 346 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Differential Geometry Through Supersymmetric Glasses by : Andrei Smilga

Download or read book Differential Geometry Through Supersymmetric Glasses written by Andrei Smilga and published by World Scientific. This book was released on 2020-06-16 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: Back in 1982, Edward Witten noticed that classical problems of differential geometry and differential topology such as the de Rham complex and Morse theory can be described in a very simple and transparent way using the language of supersymmetric quantum mechanics. Since then, many research papers have been written on this subject. Unfortunately not all the results in this field known to mathematicians have obtained a transparent physical interpretation, even if this new physical technique has also allowed many mathematical results to be derived which are completely new, in particular, hyper-Kaehler and the so-called HKT geometry. But in almost 40 years, no comprehensive monograph has appeared on this subject. So this book written by an expert in supersymmetric quantum field theories, supersymmetric quantum mechanics and its geometrical applications, addresses this yearning gap.It comprises three parts: The first, GEOMETRY, gives basic information on the geometry of real, complex, hyper-Kaehler and HKT manifolds, and is principally addressed to the physicist. The second part 'PHYSICS' presents information on classical mechanics with ordinary and Grassmann dynamics variables. Besides, the author introduces supersymmetry and dwells in particular on the representation of supersymmetry algebra in superspace. And the last and most important part of the book 'SYNTHESIS', is where the ideas borrowed from physics are used to study purely mathematical phenomena.

Differential Geometry Through Supersymmetric Glasses

Author : A. V. Smilga
Publisher :
ISBN 13 : 9789811206788
Total Pages : pages
Book Rating : 4.2/5 (67 download)

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Book Synopsis Differential Geometry Through Supersymmetric Glasses by : A. V. Smilga

Download or read book Differential Geometry Through Supersymmetric Glasses written by A. V. Smilga and published by . This book was released on 2020 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: "Back in 1982, Edward Witten noticed that classical problems of differential geometry and differential topology such as the de Rham complex and Morse theory can be described in a very simple and transparent way using the language of supersymmetric quantum mechanics. Since then, many research papers have been written on this subject. Unfortunately not all the results in this field known to mathematicians have obtained a transparent physical interpretation, even if this new physical technique has also allowed many mathematical results to be derived which are completely new, in particular, hyper-Kaehler and the so-called HKT geometry. But in almost 40 years, no comprehensive monograph has appeared on this subject. So this book written by an expert in supersymmetric quantum field theories, supersymmetric quantum mechanics and its geometrical applications, addresses this yearning gap. It comprises three parts: The first, GEOMETRY, gives basic information on the geometry of real, complex, hyper-Kaehler and HKT manifolds, and is principally addressed to the physicist. The second part "PHYSICS" presents information on classical mechanics with ordinary and Grassmann dynamics variables. Besides, the author introduces supersymmetry and dwells in particular on the representation of supersymmetry algebra in superspace. And the last and most important part of the book "SYNTHESIS", is where the ideas borrowed from physics are used to study purely mathematical phenomena"--

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.

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.

Witten Index

Author : Andrei Smilga
Publisher :
ISBN 13 : 9789811293177
Total Pages : 0 pages
Book Rating : 4.2/5 (931 download)

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Book Synopsis Witten Index by : Andrei Smilga

Download or read book Witten Index written by Andrei Smilga and published by . This book was released on 2024-08-17 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is devoted to vacuum structure of supersymmetric quantum mechanical and field theories. The Witten Index (the title of book) is a powerful theoretical tool, which allows one to find out whether supersymmetry breaks down spontaneously in a given theory or not. This is the main physical interest of this notion, but the latter has also many beautiful purely mathematical connotations. It represents a variant of the so-called equivariant index introduced by Cartan back in 1950 and is closely related to the Atiyah-Singer index.In his previous book 'Differential Geometry through Supersymmetric Glasses', World Scientific, 2020, the author showed how the supersymmetric language allows one to describe, in a rather transparent way, some known facts of differential geometry and also derive new results in this field.This book is mostly addressed to experts in quantum field theory, but the first three chapters has an introductory textbook nature and can be read by a non-expert. In Chapters 4 and 5, the general aspects of the Witten index are explained and the relationship with pure mathematical problems is elucidated. Chapters 6, 7, 8 are devoted to four-dimensional supersymmetric gauge theories: pure supersymmetric Yang-Mills theories in Chapter 6, the theories including a nonchiral (Chapter 7) and chiral (Chapter 8) matter. Chapter 9 is devoted to the so-called maximal supersymmetric quantum mechanics obtained by a dimensional reduction of the 10-dimensional supersymmetric Yang-Mills theory. In Chapter 10, the numbers of supersymmetric vacua in 3-dimensional supersymmetric Yang-Mills-Chern-Simons theories is calculated. Finally, in Chapter 11, the author discusses some relatives of the Witten index, such as the indices for the 4-dimensional theories compactified on S3 x R, rather than 4-torus or the so-called Cecolli-Fendley-Intriligator-Vafa index.

Ordinary and Stochastic Differential Geometry as a Tool for Mathematical Physics

Author : Yuri E. Gliklikh
Publisher : Springer Science & Business Media
ISBN 13 : 9401586349
Total Pages : 207 pages
Book Rating : 4.4/5 (15 download)

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Book Synopsis Ordinary and Stochastic Differential Geometry as a Tool for Mathematical Physics by : Yuri E. Gliklikh

Download or read book Ordinary and Stochastic Differential Geometry as a Tool for Mathematical Physics written by Yuri E. Gliklikh and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: The geometrical methods in modem mathematical physics and the developments in Geometry and Global Analysis motivated by physical problems are being intensively worked out in contemporary mathematics. In particular, during the last decades a new branch of Global Analysis, Stochastic Differential Geometry, was formed to meet the needs of Mathematical Physics. It deals with a lot of various second order differential equations on finite and infinite-dimensional manifolds arising in Physics, and its validity is based on the deep inter-relation between modem Differential Geometry and certain parts of the Theory of Stochastic Processes, discovered not so long ago. The foundation of our topic is presented in the contemporary mathematical literature by a lot of publications devoted to certain parts of the above-mentioned themes and connected with the scope of material of this book. There exist some monographs on Stochastic Differential Equations on Manifolds (e. g. [9,36,38,87]) based on the Stratonovich approach. In [7] there is a detailed description of It6 equations on manifolds in Belopolskaya-Dalecky form. Nelson's book [94] deals with Stochastic Mechanics and mean derivatives on Riemannian Manifolds. The books and survey papers on the Lagrange approach to Hydrodynamics [2,31,73,88], etc. , give good presentations of the use of infinite-dimensional ordinary differential geometry in ideal hydrodynamics. We should also refer here to [89,102], to the previous books by the author [53,64], and to many others.

Supergeometry, Super Riemann Surfaces and the Superconformal Action Functional

Author : Enno Keßler
Publisher : Springer
ISBN 13 : 9783030137571
Total Pages : 305 pages
Book Rating : 4.1/5 (375 download)

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Book Synopsis Supergeometry, Super Riemann Surfaces and the Superconformal Action Functional by : Enno Keßler

Download or read book Supergeometry, Super Riemann Surfaces and the Superconformal Action Functional written by Enno Keßler and published by Springer. This book was released on 2019-08-29 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book treats the two-dimensional non-linear supersymmetric sigma model or spinning string from the perspective of supergeometry. The objective is to understand its symmetries as geometric properties of super Riemann surfaces, which are particular complex super manifolds of dimension 1|1. The first part gives an introduction to the super differential geometry of families of super manifolds. Appropriate generalizations of principal bundles, smooth families of complex manifolds and integration theory are developed. The second part studies uniformization, U(1)-structures and connections on Super Riemann surfaces and shows how the latter can be viewed as extensions of Riemann surfaces by a gravitino field. A natural geometric action functional on super Riemann surfaces is shown to reproduce the action functional of the non-linear supersymmetric sigma model using a component field formalism. The conserved currents of this action can be identified as infinitesimal deformations of the super Riemann surface. This is in surprising analogy to the theory of Riemann surfaces and the harmonic action functional on them. This volume is aimed at both theoretical physicists interested in a careful treatment of the subject and mathematicians who want to become acquainted with the potential applications of this beautiful theory.

An Introduction to Differential Geometry and Topology in Mathematical Physics

Author : Rong Wang
Publisher : World Scientific
ISBN 13 : 9789810235598
Total Pages : 228 pages
Book Rating : 4.2/5 (355 download)

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Book Synopsis An Introduction to Differential Geometry and Topology in Mathematical Physics by : Rong Wang

Download or read book An Introduction to Differential Geometry and Topology in Mathematical Physics written by Rong Wang and published by World Scientific. This book was released on 1998 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives an outline of the developments of differential geometry and topology in the twentieth century, especially those which will be closely related to new discoveries in theoretical physics.

New Horizons In Differential Geometry And Its Related Fields

Author : Toshiaki Adachi
Publisher : World Scientific
ISBN 13 : 9811248117
Total Pages : 257 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis New Horizons In Differential Geometry And Its Related Fields by : Toshiaki Adachi

Download or read book New Horizons In Differential Geometry And Its Related Fields written by Toshiaki Adachi and published by World Scientific. This book was released on 2022-04-07 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents recent developments in geometric structures on Riemannian manifolds and their discretizations. With chapters written by recognized experts, these discussions focus on contact structures, Kähler structures, fiber bundle structures and Einstein metrics. It also contains works on the geometric approach on coding theory.For researchers and students, this volume forms an invaluable source to learn about these subjects that are not only in the field of differential geometry but also in other wide related areas. It promotes and deepens the study of geometric structures.

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

Author : Ilarion V. Melnikov
Publisher :
ISBN 13 : 9783030050849
Total Pages : 482 pages
Book Rating : 4.0/5 (58 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 . This book was released on 2019 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.

Supersymmetry and Equivariant de Rham Theory

Author : Victor W Guillemin
Publisher : Springer Science & Business Media
ISBN 13 : 3662039923
Total Pages : 243 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Supersymmetry and Equivariant de Rham Theory by : Victor W Guillemin

Download or read book Supersymmetry and Equivariant de Rham Theory written by Victor W Guillemin and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses the equivariant cohomology theory of differentiable manifolds. Although this subject has gained great popularity since the early 1980's, it has not before been the subject of a monograph. It covers almost all important aspects of the subject The authors are key authorities in this field.

Geometry of Supersymmetric Gauge Theories

Author : Francois Gieres
Publisher : Springer
ISBN 13 :
Total Pages : 216 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Geometry of Supersymmetric Gauge Theories by : Francois Gieres

Download or read book Geometry of Supersymmetric Gauge Theories written by Francois Gieres and published by Springer. This book was released on 1988-05-11 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph gives a detailed and pedagogical account of the geometry of rigid superspace and supersymmetric Yang-Mills theories. While the core of the text is concerned with the classical theory, the quantization and anomaly problem are briefly discussed following a comprehensive introduction to BRS differential algebras and their field theoretical applications. Among the treated topics are invariant forms and vector fields on superspace, the matrix-representation of the super-Poincarâe group, invariant connections on reductive homogeneous spaces and the supermetric approach. Various aspects of the subject are discussed for the first time in textbook and are consistently presented in a unified geometric formalism. Requiring essentially no background on supersymmetry and only a basic knowledge of differential geometry, this text will serve as a mathematically lucid introduction to supersymmetric gauge theories.

Introductory Differential Geometry For Physicists

Author : A Visconti
Publisher : World Scientific Publishing Company
ISBN 13 : 9813103884
Total Pages : 424 pages
Book Rating : 4.8/5 (131 download)

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Book Synopsis Introductory Differential Geometry For Physicists by : A Visconti

Download or read book Introductory Differential Geometry For Physicists written by A Visconti and published by World Scientific Publishing Company. This book was released on 1992-10-09 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops the mathematics of differential geometry in a way more intelligible to physicists and other scientists interested in this field. This book is basically divided into 3 levels; level 0, the nearest to intuition and geometrical experience, is a short summary of the theory of curves and surfaces; level 1 repeats, comments and develops upon the traditional methods of tensor algebra analysis and level 2 is an introduction to the language of modern differential geometry. A final chapter (chapter IV) is devoted to fibre bundles and their applications to physics. Exercises are provided to amplify the text material.

Noncommutative Differential Geometry and Its Applications to Physics

Author : Yoshiaki Maeda
Publisher : Springer Science & Business Media
ISBN 13 : 9401007047
Total Pages : 310 pages
Book Rating : 4.4/5 (1 download)

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Book Synopsis Noncommutative Differential Geometry and Its Applications to Physics by : Yoshiaki Maeda

Download or read book Noncommutative Differential Geometry and Its Applications to Physics written by Yoshiaki Maeda and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: Noncommutative differential geometry is a new approach to classical geometry. It was originally used by Fields Medalist A. Connes in the theory of foliations, where it led to striking extensions of Atiyah-Singer index theory. It also may be applicable to hitherto unsolved geometric phenomena and physical experiments. However, noncommutative differential geometry was not well understood even among mathematicians. Therefore, an international symposium on commutative differential geometry and its applications to physics was held in Japan, in July 1999. Topics covered included: deformation problems, Poisson groupoids, operad theory, quantization problems, and D-branes. The meeting was attended by both mathematicians and physicists, which resulted in interesting discussions. This volume contains the refereed proceedings of this symposium. Providing a state of the art overview of research in these topics, this book is suitable as a source book for a seminar in noncommutative geometry and physics.

Projective Differential Geometry Old and New

Author : V. Ovsienko
Publisher : Cambridge University Press
ISBN 13 : 9781139455916
Total Pages : 276 pages
Book Rating : 4.4/5 (559 download)

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Book Synopsis Projective Differential Geometry Old and New by : V. Ovsienko

Download or read book Projective Differential Geometry Old and New written by V. Ovsienko and published by Cambridge University Press. This book was released on 2004-12-13 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ideas of projective geometry keep reappearing in seemingly unrelated fields of mathematics. The authors' main goal in this 2005 book is to emphasize connections between classical projective differential geometry and contemporary mathematics and mathematical physics. They also give results and proofs of classic theorems. Exercises play a prominent role: historical and cultural comments set the basic notions in a broader context. The book opens by discussing the Schwarzian derivative and its connection to the Virasoro algebra. One-dimensional projective differential geometry features strongly. Related topics include differential operators, the cohomology of the group of diffeomorphisms of the circle, and the classical four-vertex theorem. The classical theory of projective hypersurfaces is surveyed and related to some very recent results and conjectures. A final chapter considers various versions of multi-dimensional Schwarzian derivative. In sum, here is a rapid route for graduate students and researchers to the frontiers of current research in this evergreen subject.

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.

Introduction to Supersymmetric Field Theory

Author : Sergei M. Kuzenko
Publisher :
ISBN 13 : 9780367802530
Total Pages : 656 pages
Book Rating : 4.8/5 (25 download)

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Book Synopsis Introduction to Supersymmetric Field Theory by : Sergei M. Kuzenko

Download or read book Introduction to Supersymmetric Field Theory written by Sergei M. Kuzenko and published by . This book was released on 1998 with total page 656 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ideas and Methods of Supersymmetry and Supergravity: Or a Walk Through Superspace provides a comprehensive, detailed, and self-contained account of four dimensional simple supersymmetry and supergravity. Throughout the book, the authors cultivate their material in detail with calculations and full discussions of the fundamental ideas and motivations. They develop the subject in its superfield formulations but where appropriate for illustration, analogy, and comparison with conventional field theory, they use the component formulation. The book discusses many subjects that, until now, can only be found in the research literature. In addition, it presents a plethora of new results. Combining classical and quantum field theory with group theory, differential geometry, and algebra, the book begins with a solid mathematical background that is used in the rest of the book. The next chapter covers algebraic aspects of supersymmetry and the concepts of superspace and superfield. In the following chapters, the book presents classical and quantum superfield theory and the superfield formulation of supergravity. A synthesis of results and methods developed in the book, the final chapter concludes with the theory of effective action in curved superspaces. After studying this book, readers should be well prepared to pursue independent research in any area of supersymmetry and supergravity. It will be an indispensable source of reference for advanced graduate students, postdoctoral faculty, and researchers involved in quantum field theory, high energy physics, gravity theory, mathematical physics, and applied mathematics.