Supermanifolds

Supermanifolds
Title Supermanifolds PDF eBook
Author Alice Rogers
Publisher World Scientific
Pages 262
Release 2007
Genre Mathematics
ISBN 9812708855

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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.

Supermanifolds

Supermanifolds
Title Supermanifolds PDF eBook
Author Bryce Seligman DeWitt
Publisher Cambridge University Press
Pages 432
Release 1992-05-28
Genre Mathematics
ISBN 9780521423779

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This updated and expanded second edition of an established text presents a detailed exposition of the modern theory of supermanifolds, including a rigorous account of the superanalogs of all the basic structures of ordinary manifold theory.

Supermanifolds

Supermanifolds
Title Supermanifolds PDF eBook
Author Bryce Dewitt
Publisher CUP Archive
Pages 340
Release 1984
Genre Science
ISBN 9780521311762

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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.

The Geometry of Supermanifolds

The Geometry of Supermanifolds
Title The Geometry of Supermanifolds PDF eBook
Author C. Bartocci
Publisher Springer Science & Business Media
Pages 255
Release 2012-12-06
Genre Mathematics
ISBN 9401135045

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'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.

Geometric Integration Theory on Supermanifolds

Geometric Integration Theory on Supermanifolds
Title Geometric Integration Theory on Supermanifolds PDF eBook
Author T. Voronov
Publisher CRC Press
Pages 152
Release 1991
Genre Mathematics
ISBN 9783718651993

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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.

Supermanifolds and Supergroups

Supermanifolds and Supergroups
Title Supermanifolds and Supergroups PDF eBook
Author Gijs M. Tuynman
Publisher Springer Science & Business Media
Pages 424
Release 2006-01-20
Genre Mathematics
ISBN 1402022972

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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.

Supergeometry, Super Riemann Surfaces and the Superconformal Action Functional

Supergeometry, Super Riemann Surfaces and the Superconformal Action Functional
Title Supergeometry, Super Riemann Surfaces and the Superconformal Action Functional PDF eBook
Author Enno Keßler
Publisher Springer Nature
Pages 310
Release 2019-08-28
Genre Mathematics
ISBN 3030137589

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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.