The Geometry Of Supermanifolds

Author : C. Bartocci,U. Bruzzo,Daniel Hernández-Ruipérez
Publisher : Springer Science & Business Media
Page : 255 pages
File Size : 53,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401135047

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The Geometry of Supermanifolds by C. Bartocci,U. Bruzzo,Daniel Hernández-Ruipérez Pdf

'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.

Author : Alice Rogers
Publisher : World Scientific
Page : 262 pages
File Size : 48,5 Mb
Release : 2007
Category : Mathematics
ISBN : 9789812708854

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Supermanifolds by Alice Rogers Pdf

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.

Author : T. Voronov
Publisher : CRC Press
Page : 152 pages
File Size : 47,5 Mb
Release : 1991
Category : Mathematics
ISBN : 3718651998

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Geometric Integration Theory on Supermanifolds by T. Voronov Pdf

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.

Author : Petrus J.M. Bongaarts,R. Martini
Publisher : Springer
Page : 254 pages
File Size : 48,6 Mb
Release : 2014-03-12
Category : Science
ISBN : 3662136961

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Complex Differential Geometry and Supermanifolds in Strings and Fields by Petrus J.M. Bongaarts,R. Martini Pdf

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.

Author : Gijs M. Tuynman
Publisher : Springer
Page : 416 pages
File Size : 50,7 Mb
Release : 2009-09-03
Category : Mathematics
ISBN : 9048100461

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Supermanifolds and Supergroups by Gijs M. Tuynman Pdf

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.

Author : Theodore Voronov
Publisher : Unknown
Page : 138 pages
File Size : 49,7 Mb
Release : 2014
Category : Integral geometry
ISBN : 1904868827

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Geometric Integration Theory on Supermanifolds by Theodore Voronov Pdf

Author : Gijs M. Tuynman
Publisher : Springer Science & Business Media
Page : 424 pages
File Size : 54,7 Mb
Release : 2006-01-20
Category : Mathematics
ISBN : 9781402022975

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Supermanifolds and Supergroups by Gijs M. Tuynman Pdf

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.

Author : Petrus J.M. Bongaarts,R. Martini
Publisher : Springer
Page : 268 pages
File Size : 47,6 Mb
Release : 1988-10-12
Category : Mathematics
ISBN : UCAL:B5008456

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Complex Differential Geometry and Supermanifolds in Strings and Fields by Petrus J.M. Bongaarts,R. Martini Pdf

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.

Author : Enno Keßler
Publisher : Springer Nature
Page : 305 pages
File Size : 50,9 Mb
Release : 2019-08-28
Category : Mathematics
ISBN : 9783030137588

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Supergeometry, Super Riemann Surfaces and the Superconformal Action Functional by Enno Keßler Pdf

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.

Author : Bryce Seligman DeWitt
Publisher : Cambridge University Press
Page : 432 pages
File Size : 49,7 Mb
Release : 1992-05-28
Category : Mathematics
ISBN : 0521423775

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Supermanifolds by Bryce Seligman DeWitt Pdf

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.

Author : Roberto Cianci
Publisher : Amer Inst of Physics
Page : 139 pages
File Size : 43,5 Mb
Release : 1990
Category : Science
ISBN : 8870882411

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Introduction to Supermanifolds by Roberto Cianci Pdf

Author : Claudio Carmeli,Lauren Caston,Rita Fioresi
Publisher : European Mathematical Society
Page : 308 pages
File Size : 55,5 Mb
Release : 2011
Category : Lie algebras
ISBN : 3037190973

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Mathematical Foundations of Supersymmetry by Claudio Carmeli,Lauren Caston,Rita Fioresi Pdf

Supersymmetry is a highly active area of considerable interest among physicists and mathematicians. It is not only fascinating in its own right, but there is also indication that it plays a fundamental role in the physics of elementary particles and gravitation. The purpose of the book is to lay down the foundations of the subject, providing the reader with a comprehensive introduction to the language and techniques, as well as detailed proofs and many clarifying examples. This book is aimed ideally at second-year graduate students. After the first three introductory chapters, the text is divided into two parts: the theory of smooth supermanifolds and Lie supergroups, including the Frobenius theorem, and the theory of algebraic superschemes and supergroups. There are three appendices. The first introduces Lie superalgebras and representations of classical Lie superalgebras, the second collects some relevant facts on categories, sheafification of functors and commutative algebra, and the third explains the notion of Frechet space in the super context.

Author : Stancho Dimiev,Kouei Sekigawa
Publisher : World Scientific
Page : 248 pages
File Size : 52,7 Mb
Release : 2003-06-13
Category : Mathematics
ISBN : 9789814485456

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Trends in Complex Analysis, Differential Geometry and Mathematical Physics by Stancho Dimiev,Kouei Sekigawa Pdf

' The Sixth International Workshop on Complex Structures and Vector Fields was a continuation of the previous five workshops (1992, 1994, 1996, 1998, 2000) on similar research projects. This series of workshops aims at higher achievements in studies of new research subjects. The present volume will meet with the satisfaction of many readers. Contents:Real Analytic Almost Complex Manifolds (L N Apostolova)Involutive Distributions of Codimension One in Kaehler Manifolds (G Ganchev)Three Theorems on Isotropic Immersions (S Maeda)On the Meilikhson Theorem (M S Marinov)Curvature Tensors on Almost Contact Manifolds with B-Metric (G Nakova)Complex Structures and the Quark Confinement (I B Pestov)Curvature Operators in the Relativity (V Videv & Y Tsankov)On Integrability of Almost Quaternionic Manifolds (A Yamada)and other papers Readership: Graduate students and researchers in complex analysis, differential geometry and mathematical physics. Keywords:Poincare Formulae;Oka''s Theorem;Quantum Field Theory;Time-Like Killing Vector Field;Kaehler Immersion;Circle;Integrability of Almost Hermitian Manifold;Hyperocmplex Manifold;Semi-Symmetric Space;Hypercomplex Manifold'

Author : Stancho Dimiev,Kouei Sekigawa
Publisher : World Scientific
Page : 248 pages
File Size : 48,5 Mb
Release : 2003
Category : Mathematics
ISBN : 9789812704191

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Trends in Complex Analysis, Differential Geometry, and Mathematical Physics by Stancho Dimiev,Kouei Sekigawa Pdf

The Sixth International Workshop on Complex Structures and Vector Fields was a continuation of the previous five workshops (1992, 1994, 1996, 1998, 2000) on similar research projects. This series of workshops aims at higher achievements in studies of new research subjects. The present volume will meet with the satisfaction of many readers.

Author : Yvonne Choquet-Bruhat
Publisher : Unknown
Page : 116 pages
File Size : 46,8 Mb
Release : 1989
Category : Mathematics
ISBN : UOM:39015049392692

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Graded Bundles and Supermanifolds by Yvonne Choquet-Bruhat Pdf