Supermanifolds

Theory and Applications

Author: Alice Rogers

Publisher: World Scientific

ISBN: 9812708855

Category: Mathematics

Page: 251

View: 903

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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

Author: Bryce DeWitt

Publisher: Cambridge University Press

ISBN: 9780521423779

Category: Science

Page: 407

View: 476

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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.

Geometric Integration Theory on Supermanifolds

Author: T. Voronov

Publisher: CRC Press

ISBN: 9783718651993

Category: Mathematics

Page: 138

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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

Basic Theory

Author: Gijs M. Tuynman

Publisher: Springer Science & Business Media

ISBN: 1402022972

Category: Mathematics

Page: 416

View: 5606

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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.

Complex Differential Geometry and Supermanifolds in Strings and Fields

Proceedings of the Seventh Scheveningen Conference, Scheveningen, The Netherlands, August 23–28, 1987

Author: Petrus J.M. Bongaarts,R. Martini

Publisher: Springer

ISBN: 9783662136966

Category: Science

Page: 254

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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.

Geometry in Partial Differential Equations

Author: Agostino Prastaro,Themistocles M. Rassias

Publisher: World Scientific

ISBN: 9789810214074

Category: Mathematics

Page: 465

View: 6117

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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.