Supermanifolds Theory And Applications
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| Author | : Alice Rogers |
| Publisher | : World Scientific |
| Total Pages | : 262 |
| Release | : 2007-04-18 |
| Genre | : Science |
| ISBN | : 981450503X |
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 | : C. Bartocci |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 274 |
| Release | : 1991-10-31 |
| Genre | : Mathematics |
| ISBN | : 9780792314400 |
'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 | : Bryce Seligman DeWitt |
| Publisher | : Cambridge University Press |
| Total Pages | : 432 |
| Release | : 1992-05-28 |
| Genre | : Mathematics |
| ISBN | : 9780521423779 |
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 | : Daniel S. Freed |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 132 |
| Release | : |
| Genre | : Science |
| ISBN | : 9780821871935 |
The lectures featured in this book treat fundamental concepts necessary for understanding the physics behind these mathematical applications. Freed approaches the topic with the assumption that the basic notions of supersymmetric field theory are unfamiliar to most mathematicians. He presents the material intending to impart a firm grounding in the elementary ideas.
| Author | : Bryce Dewitt |
| Publisher | : CUP Archive |
| Total Pages | : 340 |
| Release | : 1984 |
| Genre | : Science |
| ISBN | : 9780521311762 |
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.
| Author | : Gijs M. Tuynman |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 424 |
| Release | : 2006-01-20 |
| Genre | : Mathematics |
| ISBN | : 1402022972 |
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 | : Peter G. O. Freund |
| Publisher | : Cambridge University Press |
| Total Pages | : 168 |
| Release | : 1986 |
| Genre | : Science |
| ISBN | : 9780521356756 |
A brief introductory description of the new physical and mathematical ideas involved in formulating supersymmetric theories. The basic ideas are worked out in low space dimensionalities and techniques where the formulae do not obscure the concepts.
| Author | : T. Voronov |
| Publisher | : CRC Press |
| Total Pages | : 152 |
| Release | : 1991 |
| Genre | : Mathematics |
| ISBN | : 9783718651993 |
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 | : Bryce Seligman DeWitt |
| Publisher | : Cambridge University Press |
| Total Pages | : 432 |
| Release | : 1992-05-28 |
| Genre | : Mathematics |
| ISBN | : 9780521423779 |
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 | : Qing Han |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 161 |
| Release | : 2011 |
| Genre | : Mathematics |
| ISBN | : 0821853139 |
This volume is based on PDE courses given by the authors at the Courant Institute and at the University of Notre Dame, Indiana. Presented are basic methods for obtaining various a priori estimates for second-order equations of elliptic type with particular emphasis on maximal principles, Harnack inequalities, and their applications. The equations considered in the book are linear; however, the presented methods also apply to nonlinear problems.
