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Geometric Integration Theory on Supermanifolds

1991 Mathematics
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Release : 1991
Genre : Mathematics
Kind : eBook
Book Rating : 993/5 ( reviews)

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Book Synopsis Geometric Integration Theory on Supermanifolds by : T. Voronov

Download or read book Geometric Integration Theory on Supermanifolds written by T. Voronov. This book was released on 1991. 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.

Geometric Integration Theory on Supermanifolds

2014 Integral geometry
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Release : 2014
Genre : Integral geometry
Kind : eBook
Book Rating : 828/5 ( reviews)

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Book Synopsis Geometric Integration Theory on Supermanifolds by : Theodore Voronov

Download or read book Geometric Integration Theory on Supermanifolds written by Theodore Voronov. This book was released on 2014. Available in PDF, EPUB and Kindle. Book excerpt:

Supermanifolds

2007 Mathematics
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Release : 2007
Genre : Mathematics
Kind : eBook
Book Rating : 855/5 ( reviews)

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Book Synopsis Supermanifolds by : Alice Rogers

Download or read book Supermanifolds written by Alice Rogers. This book was released on 2007. 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.

Supergeometry, Super Riemann Surfaces and the Superconformal Action Functional

2019-08-28 Mathematics
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Release : 2019-08-28
Genre : Mathematics
Kind : eBook
Book Rating : 589/5 ( reviews)

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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. This book was released on 2019-08-28. 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.

Supermanifolds: Theory And Applications

2007-04-18 Science
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Release : 2007-04-18
Genre : Science
Kind : eBook
Book Rating : 03X/5 ( reviews)

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Book Synopsis Supermanifolds: Theory And Applications by : Alice Rogers

Download or read book Supermanifolds: Theory And Applications written by Alice Rogers. This book was released on 2007-04-18. 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.

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