*An Introduction*

**Author**: V. S. Varadarajan

**Publisher:**American Mathematical Soc.

**ISBN:**0821835742

**Category:**Mathematics

**Page:**300

**View:**6355

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# Search Results for: supersymmetry-for-mathematicians

*An Introduction*

**Author**: V. S. Varadarajan

**Publisher:** American Mathematical Soc.

**ISBN:** 0821835742

**Category:** Mathematics

**Page:** 300

**View:** 6355

Supersymmetry has been the object of study by theoretical physicists since the early 1970's. In recent years it has attracted the interest of mathematicians because of its novelty, and because of significance, both in mathematics and physics, of the main issues it raises. This book presents the foundations of supersymmetry to the mathematically minded reader in a cogent and self-contained manner. It begins with a brief introduction to the physical foundations of the theory, especially the classification of relativistic particles and their wave equations, such as the equations of Dirac and Weyl. It then continues the development of the theory of supermanifolds stressing the analogy with the Grothendieck theory of schemes. All the super linear algebra needed for the book is developed here and the basic theorems are established: differential and integral calculus in supermanifolds, Frobenius theorem, foundations of the theory of super Lie groups, and so on. A special feature of the book is the treatment in depth of the theory of spinors in all dimensions and signatures, which is the basis of all developments of supergeometry both in physics and mathematics, especially in quantum field theory and supergravity.
*UCLA Los Angeles, USA 2010*

**Author**: Sergio Ferrara,Rita Fioresi,Veeravalli Seshadri Varadarajan

**Publisher:** Springer Science & Business Media

**ISBN:** 3642217435

**Category:** Mathematics

**Page:** 273

**View:** 6677

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.

**Author**: Daniel S. Freed

**Publisher:** American Mathematical Soc.

**ISBN:** 9780821871935

**Category:** Science

**Page:** 119

**View:** 8083

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**: Leon Armenovich Takhtadzhi͡an

**Publisher:** American Mathematical Soc.

**ISBN:** 0821846302

**Category:** Mathematics

**Page:** 387

**View:** 8596

This book provides a comprehensive treatment of quantum mechanics from a mathematics perspective and is accessible to mathematicians starting with second-year graduate students. It addition to traditional topics, like classical mechanics, mathematical foundations of quantum mechanics, quantization, and the Schrodinger equation, this book gives a mathematical treatment of systems of identical particles with spin, and it introduces the reader to functional methods in quantum mechanics. This includes the Feynman path integral approach to quantum mechanics, integration in functional spaces, the relation between Feynman and Wiener integrals, Gaussian integration and regularized determinants of differential operators, fermion systems and integration over anticommuting (Grassmann) variables, supersymmetry and localization in loop spaces, and supersymmetric derivation of the Atiyah-Singer formula for the index of the Dirac operator. Prior to this book, mathematicians could find these topics only in physics textbooks and in specialized literature. This book is written in a concise style with careful attention to precise mathematics formulation of methods and results.Numerous problems, from routine to advanced, help the reader to master the subject. In addition to providing a fundamental knowledge of quantum mechanics, this book could also serve as a bridge for studying more advanced topics in quantum physics, among them quantum field theory. Prerequisites include standard first-year graduate courses covering linear and abstract algebra, topology and geometry, and real and complex analysis.

**Author**: Konstantin Efetov

**Publisher:** Cambridge University Press

**ISBN:** 9780521663823

**Category:** Science

**Page:** 441

**View:** 5541

This book provides a comprehensive treatment of the ideas and applications of supersymmetry.

**Author**: Jan Manschot

**Publisher:** Amsterdam University Press

**ISBN:** 9056295403

**Category:** Science

**Page:** 164

**View:** 5446

Annotation. This title can be previewed in Google Books - http://books.google.com/books?vid=ISBN9789056295400.
*Michael Marinov Memorial Volume*

**Author**: M. A. Olshanetsky,Arkady Vainshtein

**Publisher:** World Scientific

**ISBN:** 9789812777065

**Category:** Science

**Page:** 912

**View:** 9517

This book is dedicated to the memory of Michael Marinov, the theorist who, together with Felix Berezin, introduced the classical description of spin by anticommuting Grassmann variables. It contains original papers and reviews by physicists and mathematicians written specifically for the book. These articles reflect the current status and recent developments in the areas of Marinov''s research: quantum tunneling, quantization of constrained systems, supersymmetry, and others. The personal recollections included portray the human face of M Marinov, a person of great knowledge and integrity.

**Author**: I.S. Krasil'shchik,P.H. Kersten

**Publisher:** Springer Science & Business Media

**ISBN:** 9401731969

**Category:** Mathematics

**Page:** 384

**View:** 8976

To our wives, Masha and Marian Interest in the so-called completely integrable systems with infinite num ber of degrees of freedom was aroused immediately after publication of the famous series of papers by Gardner, Greene, Kruskal, Miura, and Zabusky [75, 77, 96, 18, 66, 19J (see also [76]) on striking properties of the Korteweg-de Vries (KdV) equation. It soon became clear that systems of such a kind possess a number of characteristic properties, such as infinite series of symmetries and/or conservation laws, inverse scattering problem formulation, L - A pair representation, existence of prolongation structures, etc. And though no satisfactory definition of complete integrability was yet invented, a need of testing a particular system for these properties appeared. Probably one of the most efficient tests of this kind was first proposed by Lenard [19]' who constructed a recursion operator for symmetries of the KdV equation. It was a strange operator, in a sense: being formally integro-differential, its action on the first classical symmetry (x-translation) was well-defined and produced the entire series of higher KdV equations; but applied to the scaling symmetry, it gave expressions containing terms of the type J u dx which had no adequate interpretation in the framework of the existing theories. It is not surprising that P. Olver wrote "The de duction of the form of the recursion operator (if it exists) requires a certain amount of inspired guesswork. . . " [80, p.

**Author**: Andrew Zimmerman Jones

**Publisher:** John Wiley & Sons

**ISBN:** 9780470595848

**Category:** Science

**Page:** 384

**View:** 7311

A clear, plain-English guide to this complex scientific theory String theory is the hottest topic in physics right now, with books on the subject (pro and con) flying out of the stores. String Theory For Dummies offers an accessible introduction to this highly mathematical "theory of everything," which posits ten or more dimensions in an attempt to explain the basic nature of matter and energy. Written for both students and people interested in science, this guide explains concepts, discusses the string theory's hypotheses and predictions, and presents the math in an approachable manner. It features in-depth examples and an easy-to-understand style so that readers can understand this controversial, cutting-edge theory.

**Author**: Peter C. West

**Publisher:** World Scientific

**ISBN:** 9789810200992

**Category:** Science

**Page:** 425

**View:** 7967

To the 1st edition of this monograph (addressed to advanced graduate students and researchers ) the author, responding to developments within superstring theory, has added 51/2 chapters dealing with two- dimensional supersymmetry. Authoritative, as lucid as the subject matter allows (yet demanding nonetheless!), attractively produced and priced. (NW) Annotation copyrighted by Book News, Inc., Portland, OR

**Author**: Peter G. O. Freund

**Publisher:** Cambridge University Press

**ISBN:** 9780521356756

**Category:** Science

**Page:** 152

**View:** 4074

Just as ordinary symmetries relate various forms of matter to each other, and various basic forces to each other, so the novel concept of supersymmetry relates (Fermi) matter to (Bose) force. It is the aim of this book to provide a brief introductory description of the new physical and mathematical ideas involved in formulating supersymmetric theories. The book starts with a physical motivation of supersymmetry, a presentation of the mathematics of Lie superalgebras, supergroups and superspace. Techniques for constructing manifestly globally supersymmetric field theories are given, using the superfield formalism. To allow for a clear flow of ideas, the basic ideas and techniques are worked out in low space dimensionalities where the formulae do not obscure the concepts. Generalizations to four space-time dimensions are then readily come by. Some quantum aspects are discussed. Possible phenomenological applications are not emphasized. Supergravities, locally supersymmetric theories are then considered in 4 and 11 dimensions, in component formalism. An introduction to supersymmetry will be of interest to postgraduate students and researchers in theoretical and particle physics, especially those working in quantum field theory, quantum gravity, general relativity and supergravity. The book will also be of interest to mathematicians with an interest in theoretical physics.

**Author**: Mikio Nakahara

**Publisher:** Springer-Verlag

**ISBN:** 3662453002

**Category:** Science

**Page:** 597

**View:** 3318

Differentialgeometrie und Topologie sind wichtige Werkzeuge für die Theoretische Physik. Insbesondere finden sie Anwendung in den Gebieten der Astrophysik, der Teilchen- und Festkörperphysik. Das vorliegende beliebte Buch, das nun erstmals ins Deutsche übersetzt wurde, ist eine ideale Einführung für Masterstudenten und Forscher im Bereich der theoretischen und mathematischen Physik. - Im ersten Kapitel bietet das Buch einen Überblick über die Pfadintegralmethode und Eichtheorien. - Kapitel 2 beschäftigt sich mit den mathematischen Grundlagen von Abbildungen, Vektorräumen und der Topologie. - Die folgenden Kapitel beschäftigen sich mit fortgeschritteneren Konzepten der Geometrie und Topologie und diskutieren auch deren Anwendungen im Bereich der Flüssigkristalle, bei suprafluidem Helium, in der ART und der bosonischen Stringtheorie. - Daran anschließend findet eine Zusammenführung von Geometrie und Topologie statt: es geht um Faserbündel, characteristische Klassen und Indextheoreme (u.a. in Anwendung auf die supersymmetrische Quantenmechanik). - Die letzten beiden Kapitel widmen sich der spannendsten Anwendung von Geometrie und Topologie in der modernen Physik, nämlich den Eichfeldtheorien und der Analyse der Polakov'schen bosonischen Stringtheorie aus einer gemetrischen Perspektive. Mikio Nakahara studierte an der Universität Kyoto und am King’s in London Physik sowie klassische und Quantengravitationstheorie. Heute ist er Physikprofessor an der Kinki-Universität in Osaka (Japan), wo er u. a. über topologische Quantencomputer forscht. Diese Buch entstand aus einer Vorlesung, die er während Forschungsaufenthalten an der University of Sussex und an der Helsinki University of Sussex gehalten hat.

**Author**: Daniel S. Freed,David R. Morrison,Isadore Manuel Singer

**Publisher:** American Mathematical Soc.

**ISBN:** 0821834312

**Category:** Mathematics

**Page:** 285

**View:** 2507

Each summer the IAS/Park City Mathematics Institute Graduate Summer School gathers some of the best researchers and educators in a particular field to present diverse sets of lectures. This volume presents three weeks of lectures given at the Summer School on Quantum Field Theory, Super symmetry, and Enumerative Geometry, three very active research areas in mathematics and theoretical physics. With this volume, the Park City Mathematics Institute returns to the general topic of the first institute: the interplay between quantum field theory and mathematics.Two major themes at this institute were super symmetry and algebraic geometry, particularly enumerative geometry. The volume contains two lecture series on methods of enumerative geometry that have their roots in QFT. The first series covers the Schubert calculus and quantum cohomology. The second discusses methods from algebraic geometry for computing Gromov-Witten invariants. There are also three sets of lectures of a more introductory nature: an overview of classical field theory and super symmetry, an introduction to supermanifolds, and an introduction to general relativity. This volume is recommended for independent study and is suitable for graduate students and researchers interested in geometry and physics.
*A Decade of Development*

**Author**: Peter C. West

**Publisher:** Taylor & Francis Group

**ISBN:** N.A

**Category:** Science

**Page:** 483

**View:** 7436

In this book leading developments in supersymmetry are explained by many of the subject's pioneers. In several cases the book, for the first time, allows authors to explain the important results for which they were responsible. It is primarily intended for all students and researchers in theoretical physics, mathematical physics and high energy physics who require an introduction to supersymmetric theories. It is expository and introductory in character, however the range of topics covered is sufficiently wide to be of interest to experienced researchers in supersymmetry.
*Superstrings, verborgene Dimensionen und die Suche nach der Weltformel*

**Author**: Brian Greene

**Publisher:** Siedler Verlag

**ISBN:** 3641185653

**Category:** Science

**Page:** 512

**View:** 7736

Eine hervorragende Darstellung unseres physikalischen Wissens und der Suche nach der „Weltformel“. Was ist die Superstringtheorie? Brian Greene, einer der führenden Physiker auf dem Gebiet der Superstrings, nimmt uns mit auf eine faszinierende und aufregende Reise zu den Grenzen unseres Verständnisses von Zeit, Raum und Materie.„Das elegante Universum“ ist ein populär geschriebenes und allgemein verständliches Kompendium unseres physikalischen Wissens.

**Author**: Claudio Carmeli,Lauren Caston,Rita Fioresi

**Publisher:** European Mathematical Society

**ISBN:** 9783037190975

**Category:** Mathematics

**Page:** 287

**View:** 761

**Author**: V.S. Varadarajan

**Publisher:** Springer Science & Business Media

**ISBN:** 1441906673

**Category:** Mathematics

**Page:** 236

**View:** 6957

This is a collection of essays based on lectures that author has given on various occasions on foundation of quantum theory, symmetries and representation theory, and the quantum theory of the superworld created by physicists. The lectures are linked by a unifying theme: how the quantum world and superworld appear under the lens of symmetry and supersymmetry. In the world of ultra-small times and distances such as the Planck length and Planck time, physicists believe no measurements are possible and so the structure of spacetime itself is an unknown that has to be first understood. There have been suggestions (Volovich hypothesis) that world geometry at such energy regimes is non-archimedian and some of the lectures explore the consequences of such a hypothesis. Ultimately, symmetries and supersymmetries are described by the representation of groups and supergroups. The author's interest in representation is a lifelong one and evolved slowly, and owes a great deal to conversations and discussions he had with George Mackey and Harish-Chandra. The book concludes with a retrospective look at these conversations.

**Author**: Victor W Guillemin,Shlomo Sternberg

**Publisher:** Springer Science & Business Media

**ISBN:** 3662039923

**Category:** Mathematics

**Page:** 232

**View:** 1980

This book discusses the equivariant cohomology theory of differentiable manifolds. Although this subject has gained great popularity since the early 1980's, it has not before been the subject of a monograph. It covers almost all important aspects of the subject The authors are key authorities in this field.

**Author**: Bijan Kumar Bagchi

**Publisher:** CRC Press

**ISBN:** 9781420035810

**Category:** Science

**Page:** 240

**View:** 424

Following Witten's remarkable discovery of the quantum mechanical scheme in which all the salient features of supersymmetry are embedded, SCQM (supersymmetric classical and quantum mechanics) has become a separate area of research . In recent years, progress in this field has been dramatic and the literature continues to grow. Until now, no book has offered an overview of the subject with enough detail to allow readers to become rapidly familiar with its key ideas and methods. Supersymmetry in Classical and Quantum Mechanics offers that overview and summarizes the major developments of the last 15 years. It provides both an up-to-date review of the literature and a detailed exposition of the underlying SCQM principles. For those just beginning in the field, the author presents step-by-step details of most of the computations. For more experienced readers, the treatment includes systematic analyses of more advanced topics, such as quasi- and conditional solvability and the role of supersymmetry in nonlinear systems.
*Superstrings, Anomalies and Supergravity*

**Author**: G. W. Gibbons,Stephen W. Hawking

**Publisher:** CUP Archive

**ISBN:** 9780521307215

**Category:** Science

**Page:** 481

**View:** 1384

This volume contains papers presented at the Nuffield Workshop on supersymmetry and its applications held at Cambridge in the summer of 1985 and attended by many of the leading experts in the field. In physical terms, supersymmetry is a symmetry or gauge invariance which connects bosons (particles with integer spin) with fermions (particles with half integer spin). The study of supersymmetry has led to the construction of Yang-Mills theories, which are the first field theories to be free of the divergences that usually occur in quantum theories, with an infinite number of degrees of freedom. It has also led to the construction of supergravity and superstring theories which seem to be the best hope for a complete unified theory of all physical interactions including gravity. Supersymmetry and its Applications reviews a number of recent advances in the area of anomalies, the topology of gauge theories, superstrings, supergravity and super Yang-Mills theory.The papers, written by both physicists and mathematicians, include both expository articles and progress reports describing most recent developments.

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