Supermanifolds And Supergroups

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Supermanifolds and Supergroups

Gijs M. Tuynman
Supermanifolds and Supergroups Book PDF

Author : Gijs M. Tuynman
Publisher : Springer Science & Business Media
Page : 424 pages
File Size : 47,9 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.

Supermanifolds and Supergroups

Gijs M. Tuynman
Supermanifolds and Supergroups Book PDF

Author : Gijs M. Tuynman
Publisher : Springer
Page : 416 pages
File Size : 45,6 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.

The Geometry of Supermanifolds

C. Bartocci,U. Bruzzo,Daniel Hernández-Ruipérez
The Geometry of Supermanifolds Book PDF

Author : C. Bartocci,U. Bruzzo,Daniel Hernández-Ruipérez
Publisher : Springer Science & Business Media
Page : 255 pages
File Size : 44,8 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.

Geometric Integration Theory on Supermanifolds

T. Voronov
Geometric Integration Theory on Supermanifolds Book PDF

Author : T. Voronov
Publisher : CRC Press
Page : 152 pages
File Size : 45,9 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.

Chevalley Supergroups

Rita Fioresi,Fabio Gavarini
Chevalley Supergroups Book PDF

Author : Rita Fioresi,Fabio Gavarini
Publisher : American Mathematical Soc.
Page : 77 pages
File Size : 41,9 Mb
Release : 2012
Category : Chevalley groups
ISBN : 9780821853009

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Chevalley Supergroups by Rita Fioresi,Fabio Gavarini Pdf

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.

Noncommutative Structures in Mathematics and Physics

S. Duplij,Julius Wess
Noncommutative Structures in Mathematics and Physics Book PDF

Author : S. Duplij,Julius Wess
Publisher : Springer Science & Business Media
Page : 472 pages
File Size : 50,6 Mb
Release : 2012-12-06
Category : Science
ISBN : 9789401008365

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Noncommutative Structures in Mathematics and Physics by S. Duplij,Julius Wess Pdf

A presentation of outstanding achievements and ideas, of both eastern and western scientists, both mathematicians and physicists. Their presentations of recent work on quantum field theory, supergravity, M-theory, black holes and quantum gravity, together with research into noncommutative geometry, Hopf algebras, representation theory, categories and quantum groups, take the reader to the forefront of the latest developments. Other topics covered include supergravity and branes, supersymmetric quantum mechanics and superparticles, (super) black holes, superalgebra representations, and SUSY GUT phenomenology. Essential reading for workers in the modern methods of theoretical and mathematical physics.

Supergravity And Superstrings: A Geometric Perspective (In 3 Volumes)

Castellani Leonardo,D'auria Riccardo,Fre Pietro
Supergravity And Superstrings A Geometric Perspective In 3 Volumes Book PDF

Author : Castellani Leonardo,D'auria Riccardo,Fre Pietro
Publisher : World Scientific Publishing Company
Page : 2216 pages
File Size : 54,5 Mb
Release : 1991-06-11
Category : Electronic
ISBN : 9789814590730

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Supergravity And Superstrings: A Geometric Perspective (In 3 Volumes) by Castellani Leonardo,D'auria Riccardo,Fre Pietro Pdf

This book provides a self-contained presentation of supergravity theories from its fundamentals to its most recent union with string and superstring theories, which are also reviewed in a self-contained manner. The subject is presented consistently in a unified geometric formalism, relying on the calculus of exterior forms and the mathematics needed to develop the theory is explained in appropriate chapters.

Classical Lie Algebras at Infinity

Ivan Penkov,Crystal Hoyt
Classical Lie Algebras at Infinity Book PDF

Author : Ivan Penkov,Crystal Hoyt
Publisher : Springer Nature
Page : 245 pages
File Size : 46,7 Mb
Release : 2022-01-05
Category : Mathematics
ISBN : 9783030896607

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Classical Lie Algebras at Infinity by Ivan Penkov,Crystal Hoyt Pdf

Originating from graduate topics courses given by the first author, this book functions as a unique text-monograph hybrid that bridges a traditional graduate course to research level representation theory. The exposition includes an introduction to the subject, some highlights of the theory and recent results in the field, and is therefore appropriate for advanced graduate students entering the field as well as research mathematicians wishing to expand their knowledge. The mathematical background required varies from chapter to chapter, but a standard course on Lie algebras and their representations, along with some knowledge of homological algebra, is necessary. Basic algebraic geometry and sheaf cohomology are needed for Chapter 10. Exercises of various levels of difficulty are interlaced throughout the text to add depth to topical comprehension. The unifying theme of this book is the structure and representation theory of infinite-dimensional locally reductive Lie algebras and superalgebras. Chapters 1-6 are foundational; each of the last 4 chapters presents a self-contained study of a specialized topic within the larger field. Lie superalgebras and flag supermanifolds are discussed in Chapters 3, 7, and 10, and may be skipped by the reader.

The Schrödinger Equation

F.A. Berezin,M. Shubin
The Schr dinger Equation Book PDF

Author : F.A. Berezin,M. Shubin
Publisher : Springer Science & Business Media
Page : 573 pages
File Size : 41,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401131544

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The Schrödinger Equation by F.A. Berezin,M. Shubin Pdf

This volume deals with those topics of mathematical physics, associated with the study of the Schrödinger equation, which are considered to be the most important. Chapter 1 presents the basic concepts of quantum mechanics. Chapter 2 provides an introduction to the spectral theory of the one-dimensional Schrödinger equation. Chapter 3 opens with a discussion of the spectral theory of the multi-dimensional Schrödinger equation, which is a far more complex case and requires careful consideration of aspects which are trivial in the one-dimensional case. Chapter 4 presents the scattering theory for the multi-dimensional non-relativistic Schrödinger equation, and the final chapter is devoted to quantization and Feynman path integrals. These five main chapters are followed by three supplements, which present material drawn on in the various chapters. The first two supplements deal with general questions concerning the spectral theory of operators in Hilbert space, and necessary information relating to Sobolev spaces and elliptic equations. Supplement 3, which essentially stands alone, introduces the concept of the supermanifold which leads to a more natural treatment of quantization. Although written primarily for mathematicians who wish to gain a better awareness of the physical aspects of quantum mechanics and related topics, it will also be useful for mathematical physicists who wish to become better acquainted with the mathematical formalism of quantum mechanics. Much of the material included here has been based on lectures given by the authors at Moscow State University, and this volume can also be recommended as a supplementary graduate level introduction to the spectral theory of differential operators with both discrete and continuous spectra. This English edition is a revised, expanded version of the original Soviet publication.

Advances in Lie Superalgebras

Maria Gorelik,Paolo Papi
Advances in Lie Superalgebras Book PDF

Author : Maria Gorelik,Paolo Papi
Publisher : Springer Science & Business
Page : 281 pages
File Size : 40,9 Mb
Release : 2014-04-28
Category : Mathematics
ISBN : 9783319029528

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Advances in Lie Superalgebras by Maria Gorelik,Paolo Papi Pdf

The volume is the outcome of the conference "Lie superalgebras," which was held at the Istituto Nazionale di Alta Matematica, in 2012. The conference gathered many specialists in the subject, and the talks held provided comprehensive insights into the newest trends in research on Lie superalgebras (and related topics like vertex algebras, representation theory and supergeometry). The book contains contributions of many leading esperts in the field and provides a complete account of the newest trends in research on Lie Superalgebras.

Mathematical Foundations of Supersymmetry

Claudio Carmeli,Lauren Caston,Rita Fioresi
Mathematical Foundations of Supersymmetry Book PDF

Author : Claudio Carmeli,Lauren Caston,Rita Fioresi
Publisher : European Mathematical Society
Page : 308 pages
File Size : 47,8 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.

Supersymmetry in Mathematics and Physics

Sergio Ferrara,Rita Fioresi,Veeravalli Seshadri Varadarajan
Supersymmetry in Mathematics and Physics Book PDF

Author : Sergio Ferrara,Rita Fioresi,Veeravalli Seshadri Varadarajan
Publisher : Springer Science & Business Media
Page : 279 pages
File Size : 44,9 Mb
Release : 2011-08-28
Category : Mathematics
ISBN : 9783642217432

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Supersymmetry in Mathematics and Physics by Sergio Ferrara,Rita Fioresi,Veeravalli Seshadri Varadarajan Pdf

Supersymmetry was created by the physicists in the 1970's to give a unified treatment of fermions and bosons, the basic constituents of matter. Since then its mathematical structure has been recognized as that of a new development in geometry, and mathematicians have busied themselves with exploring this aspect. This volume collects recent advances in this field, both from a physical and a mathematical point of view, with an accent on a rigorous treatment of the various questions raised.

Perspectives in Lie Theory

Filippo Callegaro,Giovanna Carnovale,Fabrizio Caselli,Corrado De Concini,Alberto De Sole
Perspectives in Lie Theory Book PDF

Author : Filippo Callegaro,Giovanna Carnovale,Fabrizio Caselli,Corrado De Concini,Alberto De Sole
Publisher : Springer
Page : 461 pages
File Size : 48,5 Mb
Release : 2017-12-07
Category : Mathematics
ISBN : 9783319589718

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Perspectives in Lie Theory by Filippo Callegaro,Giovanna Carnovale,Fabrizio Caselli,Corrado De Concini,Alberto De Sole Pdf

Lie theory is a mathematical framework for encoding the concept of symmetries of a problem, and was the central theme of an INdAM intensive research period at the Centro de Giorgi in Pisa, Italy, in the academic year 2014-2015. This book gathers the key outcomes of this period, addressing topics such as: structure and representation theory of vertex algebras, Lie algebras and superalgebras, as well as hyperplane arrangements with different approaches, ranging from geometry and topology to combinatorics.

Geometric Methods in Physics

Piotr Kielanowski,S. Twareque Ali,Anatol Odzijewicz,Martin Schlichenmaier,Theodore Voronov
Geometric Methods in Physics Book PDF

Author : Piotr Kielanowski,S. Twareque Ali,Anatol Odzijewicz,Martin Schlichenmaier,Theodore Voronov
Publisher : Springer Science & Business Media
Page : 432 pages
File Size : 53,5 Mb
Release : 2012-11-05
Category : Mathematics
ISBN : 9783034804486

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Geometric Methods in Physics by Piotr Kielanowski,S. Twareque Ali,Anatol Odzijewicz,Martin Schlichenmaier,Theodore Voronov Pdf

The Białowieża workshops on Geometric Methods in Physics are among the most important meetings in the field. Every year some 80 to 100 participants from both mathematics and physics join to discuss new developments and to interchange ideas. This volume contains contributions by selected speakers at the XXX meeting in 2011 as well as additional review articles and shows that the workshop remains at the cutting edge of ongoing research. The 2011 workshop focussed on the works of the late Felix A. Berezin (1931–1980) on the occasion of his 80th anniversary as well as on Bogdan Mielnik and Stanisław Lech Woronowicz on their 75th and 70th birthday, respectively. The groundbreaking work of Berezin is discussed from today’s perspective by presenting an overview of his ideas and their impact on further developments. He was, among other fields, active in representation theory, general concepts of quantization and coherent states, supersymmetry and supermanifolds. Another focus lies on the accomplishments of Bogdan Mielnik and Stanisław Lech Woronowicz. Mielnik’s geometric approach to the description of quantum mixed states, the method of quantum state manipulation and their important implications for quantum computing and quantum entanglement are discussed as well as the intricacies of the quantum time operator. Woronowicz’ fruitful notion of a compact quantum group and related topics are also addressed.

Collected Papers II

Israel M. Gelfand
Collected Papers II Book PDF

Author : Israel M. Gelfand
Publisher : Springer Science & Business Media
Page : 1060 pages
File Size : 49,6 Mb
Release : 1988-09-09
Category : Mathematics
ISBN : 354019035X

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Collected Papers II by Israel M. Gelfand Pdf

I.M. Gelfand (1913 - 2009), one of the world's leading contemporary mathematicians, largely determined the modern view of functional analysis with its numerous relations to other branches of mathematics, including mathematical physics, algebra, topology, differential geometry and analysis. In this three-volume Collected Papers Gelfand presents a representative sample of his work. Gelfand's research led to the development of remarkable mathematical theories - most of which are now classics - in the field of Banach algebras, infinite-dimensional representations of Lie groups, the inverse Sturm-Liouville problem, cohomology of infinite-dimensional Lie algebras, integral geometry, generalized functions and general hypergeometric functions. The corresponding papers form the major part of the collection. Some articles on numerical methods and cybernetics as well as a few on biology are also included. A substantial number of the papers have been translated into English especially for this edition. The collection is rounded off by an extensive bibliography with almost 500 references. Gelfand's Collected Papers will be a great stimulus, especially for the younger generation, and will provide a strong incentive to researchers.