Supermanifolds Theory And Applications

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Supermanifolds

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Author : Alice Rogers
language : en
Publisher: World Scientific
Release Date : 2007

Supermanifolds written by Alice Rogers and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.

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 Theory And Applications

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Author : Alice Rogers
language : en
Publisher: World Scientific
Release Date : 2007-04-18

Supermanifolds Theory And Applications written by Alice Rogers and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-04-18 with Science categories.

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.

The Geometry Of Supermanifolds

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Author : C. Bartocci
language : en
Publisher: Springer Science & Business Media
Release Date : 1991-10-31

The Geometry Of Supermanifolds written by C. Bartocci and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-10-31 with Mathematics categories.

'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.

Supermanifolds

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Author : Bryce Seligman DeWitt
language : en
Publisher: Cambridge University Press
Release Date : 1992-05-28

Supermanifolds written by Bryce Seligman DeWitt and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-05-28 with Mathematics categories.

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

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Author : Bryce Dewitt
language : en
Publisher: CUP Archive
Release Date : 1984

Supermanifolds written by Bryce Dewitt and has been published by CUP Archive this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Science categories.

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.

Supergeometry Super Riemann Surfaces And The Superconformal Action Functional

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Author : Enno Keßler
language : en
Publisher: Springer Nature
Release Date : 2019-08-28

Supergeometry Super Riemann Surfaces And The Superconformal Action Functional written by Enno Keßler and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-08-28 with Mathematics categories.

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.

The Geometry Of Supermanifolds

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Author : C. Bartocci
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

The Geometry Of Supermanifolds written by C. Bartocci and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

'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.

An Eventful Journey To Unification Of All The Fundamental Forces

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Author : Robert Delbourgo
language : en
Publisher: World Scientific
Release Date : 2019-12-19

An Eventful Journey To Unification Of All The Fundamental Forces written by Robert Delbourgo and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-12-19 with Science categories.

During the last years of his life Einstein tried unsuccessfully to unify electromagnetic force with gravitational force geometrically. The nearest he got was through the ideas of Kaluza and Klein who appended a tiny fifth commuting coordinate to spacetime. Researchers have followed in those footsteps by adding at least six more such minuscule coordinates so as to incorporate the other forces of nature, culminating in string theory — which has unfortunately not met with experimental support. Other proposals have likewise failed or are still waiting to be confirmed experimentally.The author shows that one can successfully unify gravity with electromagnetism geometrically by adding a single complex anticommuting coordinate to spacetime, which can be associated with the property of 'electricity'. By adding extra four anticommuting properties ('chromicity' and 'neutrinicity'), associated with strong and weak interactions, one can get a unified picture of all the natural forces and particles including the 'standard model': The whole construct relies upon the full specification of events and automatically allows for replication of particle families. The monograph traces the history of attempts of unification before explaining the author's 'where-when-what' scheme.

Supermanifolds And Supergroups

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Author : Gijs M. Tuynman
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-01-20

Supermanifolds And Supergroups written by Gijs M. Tuynman and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-01-20 with Mathematics categories.

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.

Chevalley Supergroups

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Author : Rita Fioresi
language : en
Publisher: American Mathematical Soc.
Release Date : 2012

Chevalley Supergroups written by Rita Fioresi and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.

In the framework of algebraic supergeometry, the authors give a construction of the scheme-theoretic supergeometric analogue of split reductive algebraic group-schemes, namely affine algebraic supergroups associated to simple Lie superalgebras of classical type. In particular, all Lie superalgebras of both basic and strange types are considered. This provides a unified approach to most of the algebraic supergroups considered so far in the literature, and an effective method to construct new ones. The authors' method follows the pattern of a suitable scheme-theoretic revisitation of Chevalley's construction of semisimple algebraic groups, adapted to the reductive case. As an intermediate step, they prove an existence theorem for Chevalley bases of simple classical Lie superalgebras and a PBW-like theorem for their associated Kostant superalgebras.