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The Geometry Of Supermanifolds
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Book Synopsis The Geometry of Supermanifolds by : C. Bartocci
Download or read book The Geometry of Supermanifolds written by C. Bartocci and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'Et moi ... - si favait III mmment en revenir, One service mathematics has rendered the je n'y serais point aile:' human race. It has put CXlUImon sense back Iules Verne where it belongs. on the topmost shelf next to the dUlty canister lahelled 'discarded non- The series i. divergent; therefore we may be able to do something with it. Eric T. Bell O. Hesvi.ide Mathematics is a tool for thOUght. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d't!tre of this series.
Download or read book Supermanifolds written by Alice Rogers and published by World Scientific. This book was released on 2007 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book aims to fill the gap in the available literature on supermanifolds, describing the different approaches to supermanifolds together with various applications to physics, including some which rely on the more mathematical aspects of supermanifold theory. The first part of the book contains a full introduction to the theory of supermanifolds, comparing and contrasting the different approaches that exist. Topics covered include tensors on supermanifolds, super fibre bundles, super Lie groups and integration theory. Later chapters emphasise applications, including the superspace approach to supersymmetric theories, super Riemann surfaces and the spinning string, path integration on supermanifolds and BRST quantization.
Book Synopsis Supermanifolds and Supergroups by : Gijs M. Tuynman
Download or read book Supermanifolds and Supergroups written by Gijs M. Tuynman and published by Springer Science & Business Media. This book was released on 2006-01-20 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: Supermanifolds and Supergroups explains the basic ingredients of super manifolds and super Lie groups. It starts with super linear algebra and follows with a treatment of super smooth functions and the basic definition of a super manifold. When discussing the tangent bundle, integration of vector fields is treated as well as the machinery of differential forms. For super Lie groups the standard results are shown, including the construction of a super Lie group for any super Lie algebra. The last chapter is entirely devoted to super connections. The book requires standard undergraduate knowledge on super differential geometry and super Lie groups.
Book Synopsis Geometric Integration Theory on Supermanifolds by : T. Voronov
Download or read book Geometric Integration Theory on Supermanifolds written by T. Voronov and published by CRC Press. This book was released on 1991 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author presents the first detailed and original account of his theory of forms on supermanifolds-a correct and non-trivial analogue of Cartan-de Rham theory based on new concepts. The paper develops the apparatus of supermanifold differential topology necessary for the integration theory. A key feature is the identification of a class of proper morphisms intimately connected with Berezin integration, which are of fundamental importance in various problems. The work also contains a condensed introduction to superanalysis and supermanifolds, free from algebraic formalism, which sets out afresh such challenging problems as the Berezin intgegral on a bounded domain.
Book Synopsis Complex Differential Geometry and Supermanifolds in Strings and Fields by : Petrus J.M. Bongaarts
Download or read book Complex Differential Geometry and Supermanifolds in Strings and Fields written by Petrus J.M. Bongaarts and published by Springer. This book was released on 1988-10-12 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume deals with one of the most active fields of research in mathematical physics: the use of geometric and topological methods in field theory. The emphasis in these proceedings is on complex differential geometry, in particular on Kähler manifolds, supermanifolds, and graded manifolds. From the point of view of physics the main topics were field theory, string theory and problems from elementary particle theory involving supersymmetry. The lectures show a remarkable unity of approach and are considerably related to each other. They should be of great value to researchers and graduate students.
Book Synopsis Supermanifolds and Supergroups by : Gijs M. Tuynman
Download or read book Supermanifolds and Supergroups written by Gijs M. Tuynman and published by Springer. This book was released on 2009-09-03 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: Supermanifolds and Supergroups explains the basic ingredients of super manifolds and super Lie groups. It starts with super linear algebra and follows with a treatment of super smooth functions and the basic definition of a super manifold. When discussing the tangent bundle, integration of vector fields is treated as well as the machinery of differential forms. For super Lie groups the standard results are shown, including the construction of a super Lie group for any super Lie algebra. The last chapter is entirely devoted to super connections. The book requires standard undergraduate knowledge on super differential geometry and super Lie groups.
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 Nature. This book was released on 2019-08-28 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.
Book Synopsis The Geometry of Four-manifolds by : S. K. Donaldson
Download or read book The Geometry of Four-manifolds written by S. K. Donaldson and published by Oxford University Press, USA. This book was released on 1990 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text provides an accessible account to the modern study of the geometry of four-manifolds. Prerequisites are a firm grounding in differential topology and geometry, as may be gained from the first year of a graduate course.
Book Synopsis Geometry and Topology of Manifolds by : Hans U. Boden
Download or read book Geometry and Topology of Manifolds written by Hans U. Boden and published by American Mathematical Soc.. This book was released on 2005 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains expository papers that give an up-to-date account of recent developments and open problems in the geometry and topology of manifolds, along with several research articles that present new results appearing in published form for the first time. The unifying theme is the problem of understanding manifolds in low dimensions, notably in dimensions three and four, and the techniques include algebraic topology, surgery theory, Donaldson and Seiberg-Witten gauge theory,Heegaard Floer homology, contact and symplectic geometry, and Gromov-Witten invariants. The articles collected for this volume were contributed by participants of the Conference "Geometry and Topology of Manifolds" held at McMaster University on May 14-18, 2004 and are representative of the manyexcellent talks delivered at the conference.
Book Synopsis Riemannian Topology and Geometric Structures on Manifolds by : Krzysztof Galicki
Download or read book Riemannian Topology and Geometric Structures on Manifolds written by Krzysztof Galicki and published by Springer Science & Business Media. This book was released on 2010-07-25 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: Riemannian Topology and Structures on Manifolds results from a similarly entitled conference held on the occasion of Charles P. Boyer’s 65th birthday. The various contributions to this volume discuss recent advances in the areas of positive sectional curvature, Kähler and Sasakian geometry, and their interrelation to mathematical physics, especially M and superstring theory. Focusing on these fundamental ideas, this collection presents review articles, original results, and open problems of interest.
Book Synopsis The Geometry of Curvature Homogeneous Pseudo-Riemannian Manifolds by : Peter B. Gilkey
Download or read book The Geometry of Curvature Homogeneous Pseudo-Riemannian Manifolds written by Peter B. Gilkey and published by World Scientific. This book was released on 2007 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Pseudo-Riemannian geometry is an active research field not only in differential geometry but also in mathematical physics where the higher signature geometries play a role in brane theory. An essential reference tool for research mathematicians and physicists, this book also serves as a useful introduction to students entering this active and rapidly growing field. The author presents a comprehensive treatment of several aspects of pseudo-Riemannian geometry, including the spectral geometry of the curvature tensor, curvature homogeneity, and Stanilov-Tsankov-Videv theory."--BOOK JACKET.
Book Synopsis Geometry in Partial Differential Equations by : Agostino Prastaro
Download or read book Geometry in Partial Differential Equations written by Agostino Prastaro and published by World Scientific. This book was released on 1994 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book emphasizes the interdisciplinary interaction in problems involving geometry and partial differential equations. It provides an attempt to follow certain threads that interconnect various approaches in the geometric applications and influence of partial differential equations. A few such approaches include: Morse-Palais-Smale theory in global variational calculus, general methods to obtain conservation laws for PDEs, structural investigation for the understanding of the meaning of quantum geometry in PDEs, extensions to super PDEs (formulated in the category of supermanifolds) of the geometrical methods just introduced for PDEs and the harmonic theory which proved to be very important especially after the appearance of the Atiyah-Singer index theorem, which provides a link between geometry and topology.
Book Synopsis Super Differential Geometry by : Thomas Schmitt
Download or read book Super Differential Geometry written by Thomas Schmitt and published by . This book was released on 1984 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Differential Geometry in the Large by : Owen Dearricott
Download or read book Differential Geometry in the Large written by Owen Dearricott and published by Cambridge University Press. This book was released on 2020-10-22 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: From Ricci flow to GIT, physics to curvature bounds, Sasaki geometry to almost formality. This is differential geometry at large.
Book Synopsis Introduction to Symplectic Geometry by : Jean-Louis Koszul
Download or read book Introduction to Symplectic Geometry written by Jean-Louis Koszul and published by Springer. This book was released on 2019-04-15 with total page 121 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introductory book offers a unique and unified overview of symplectic geometry, highlighting the differential properties of symplectic manifolds. It consists of six chapters: Some Algebra Basics, Symplectic Manifolds, Cotangent Bundles, Symplectic G-spaces, Poisson Manifolds, and A Graded Case, concluding with a discussion of the differential properties of graded symplectic manifolds of dimensions (0,n). It is a useful reference resource for students and researchers interested in geometry, group theory, analysis and differential equations.This book is also inspiring in the emerging field of Geometric Science of Information, in particular the chapter on Symplectic G-spaces, where Jean-Louis Koszul develops Jean-Marie Souriau's tools related to the non-equivariant case of co-adjoint action on Souriau’s moment map through Souriau’s Cocycle, opening the door to Lie Group Machine Learning with Souriau-Fisher metric.
Book Synopsis Complex Differential Geometry and Supermanifolds in Strings and Fields by : Petrus J.M. Bongaarts
Download or read book Complex Differential Geometry and Supermanifolds in Strings and Fields written by Petrus J.M. Bongaarts and published by Springer. This book was released on 1988-10-12 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume deals with one of the most active fields of research in mathematical physics: the use of geometric and topological methods in field theory. The emphasis in these proceedings is on complex differential geometry, in particular on Kähler manifolds, supermanifolds, and graded manifolds. From the point of view of physics the main topics were field theory, string theory and problems from elementary particle theory involving supersymmetry. The lectures show a remarkable unity of approach and are considerably related to each other. They should be of great value to researchers and graduate students.
Download or read book Supermanifolds written by Bryce Dewitt and published by CUP Archive. This book was released on 1984 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a detailed exposition of the modern theory of supermanifolds, including a rigorous account of the super-analogs of all the basic structures of ordinary manifold theory. The exposition opens with the theory of analysis over supernumbers (Grassmann variables), Berezin integration, supervector spaces and the superdeterminant. This basic material is then applied to the theory of supermanifolds, with an account of the super-analog of Lie derivatives, connections, metrics, curvature, geodesics, Killing flows, conformal groups, etc. The book goes on to discuss the theory of super Lie groups, super Lie algebras, and invariant geometrical structures on coset spaces. Complete descriptions are given of all the simple super Lie groups. The final chapter contains an account of the Peierls bracket for superclassical dynamical systems, super Hilbert spaces, path integration for fermionic quantum systems, and simple models of Bose-Fermi supersymmetry. Many exercises are included to supplement the material in the text.
