Mathematical Aspects Of Superspace

Author : H.J. Seifert,C.J.S. Clarke,A. Rosenblum
Publisher : Springer Science & Business Media
Page : 220 pages
File Size : 47,7 Mb
Release : 2012-12-06
Category : Science
ISBN : 9789400964464

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Mathematical Aspects of Superspace by H.J. Seifert,C.J.S. Clarke,A. Rosenblum Pdf

Over the past five years, through a continually increasing wave of activity in the physics community, supergravity has come to be regarded as one of the most promising ways of unifying gravity with other particle interaction as a finite gauge theory to explain the spectrum of elementary particles. Concurrently im portant mathematical works on the arena of supergravity has taken place, starting with Kostant's theory of graded manifolds and continuing with Batchelor's work linking this with the superspace formalism. There remains, however, a gap between the mathematical and physical approaches expressed by such unanswered questions as, does there exist a superspace having all the properties that physicists require of it? Does it make sense to perform path integral in such a space? It is hoped that these proceedings will begin a dialogue between mathematicians and physicists on such questions as the plan of renormalisation in supergravity. The contributors to the proceedings consist both of mathe maticians and relativists who bring their experience in differen tial geometry, classical gravitation and algebra and also quantum field theorists specialized in supersymmetry and supergravity. One of the most important problems associated with super symmetry is its relationship to the elementary particle spectrum.

Author : Alice Rogers
Publisher : World Scientific
Page : 262 pages
File Size : 52,5 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 : Michiel Hazewinkel
Publisher : Springer Science & Business Media
Page : 556 pages
File Size : 52,7 Mb
Release : 1993-01-31
Category : Mathematics
ISBN : 9781556080081

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Encyclopaedia of Mathematics by Michiel Hazewinkel Pdf

This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fme subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.

Author : N. H. March
Publisher : Academic Press
Page : 651 pages
File Size : 52,9 Mb
Release : 2013-10-22
Category : Mathematics
ISBN : 9781483288376

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Supersymmetries and Infinite-Dimensional Algebras by N. H. March Pdf

Recent devopments, particularly in high-energy physics, have projected group theory and symmetry consideration into a central position in theoretical physics. These developments have taken physicists increasingly deeper into the fascinating world of pure mathematics. This work presents important mathematical developments of the last fifteen years in a form that is easy to comprehend and appreciate.

Author : Mark J. Gotay,Jerrold E. Marsden,Vincent Moncrief
Publisher : American Mathematical Soc.
Page : 658 pages
File Size : 40,9 Mb
Release : 1992
Category : Science
ISBN : 9780821851449

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Mathematical Aspects of Classical Field Theory by Mark J. Gotay,Jerrold E. Marsden,Vincent Moncrief Pdf

Classical field theory has undergone a renaissance in recent years. Symplectic techniques have yielded deep insights into its foundations, as has an improved understanding of the variational calculus. Further impetus for the study of classical fields has come from other areas, such as integrable systems, Poisson geometry, global analysis, and quantum theory. This book contains the proceedings of the AMS-IMS-SIAM Joint Summer Research Conference on Mathematical Aspects of Classical Field Theory, held in July 1991 at the University of Washington at Seattle. The conference brought together researchers in many of the main areas of classical field theory to present the latest ideas and results. The volume contains thirty refereed papers, both survey and research articles, and is designed to reflect the state of the art as well as chart the future course of the subject. The topics fall into four major categories: global analysis and relativity (cosmic censorship, initial value problem, quantum gravity), geometric methods (symplectic and Poisson structures, momentum mappings, Dirac constraint theory), BRST theory, and the calculus of variations (the variational bicomplex, higher order theories). Also included are related topics with a ``classical basis'', such as geometric quantization, integrable systems, symmetries, deformation theory, and geometric mechanics.

Author : A. S. Galperin,E. A. Ivanov,V. I. Ogievetsky,E. S. Sokatchev
Publisher : Cambridge University Press
Page : 322 pages
File Size : 45,9 Mb
Release : 2001-09-27
Category : Science
ISBN : 9781139430494

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Harmonic Superspace by A. S. Galperin,E. A. Ivanov,V. I. Ogievetsky,E. S. Sokatchev Pdf

Inspired by exciting developments in superstring theory, this is a pedagogical and comprehensive introduction to the harmonic superspace method in extended supersymmetry. The authors (credited with inventing the technique) are recognised as world experts on the subject and present a clear account of its formalism and applications.

Author : Anonim
Publisher : Unknown
Page : 796 pages
File Size : 42,7 Mb
Release : 2006
Category : Mathematics
ISBN : UOM:39015067268402

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Mathematical Reviews by Anonim Pdf

Author : Tan Chung-i,Jevicki Antal
Publisher : World Scientific
Page : 1092 pages
File Size : 55,8 Mb
Release : 1989-05-01
Category : Electronic
ISBN : 9789814590778

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Particles, Strings And Supernovae - Proceedings Of Theoretical Advanced Study Institute In Elementary Particle Physics (In 2 Volumes) by Tan Chung-i,Jevicki Antal Pdf

Author : Bryce Seligman DeWitt
Publisher : Cambridge University Press
Page : 432 pages
File Size : 51,5 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 : Andrei Y. Khrennikov
Publisher : Springer Science & Business Media
Page : 359 pages
File Size : 55,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401146098

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Superanalysis by Andrei Y. Khrennikov Pdf

defined as elements of Grassmann algebra (an algebra with anticom muting generators). The derivatives of these elements with respect to anticommuting generators were defined according to algebraic laws, and nothing like Newton's analysis arose when Martin's approach was used. Later, during the next twenty years, the algebraic apparatus de veloped by Martin was used in all mathematical works. We must point out here the considerable contribution made by F. A. Berezin, G 1. Kac, D. A. Leites, B. Kostant. In their works, they constructed a new division of mathematics which can naturally be called an algebraic superanalysis. Following the example of physicists, researchers called the investigations carried out with the use of commuting and anticom muting coordinates supermathematics; all mathematical objects that appeared in supermathematics were called superobjects, although, of course, there is nothing "super" in supermathematics. However, despite the great achievements in algebraic superanaly sis, this formalism could not be regarded as a generalization to the case of commuting and anticommuting variables from the ordinary Newton analysis. What is more, Schwinger's formalism was still used in practically all physical works, on an intuitive level, and physicists regarded functions of anticommuting variables as "real functions" == maps of sets and not as elements of Grassmann algebras. In 1974, Salam and Strathdee proposed a very apt name for a set of super points. They called this set a superspace.

Author : Huaizhong Zhao,Aubrey Truman
Publisher : World Scientific
Page : 458 pages
File Size : 53,8 Mb
Release : 2012
Category : Mathematics
ISBN : 9789814360913

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New Trends in Stochastic Analysis and Related Topics by Huaizhong Zhao,Aubrey Truman Pdf

The volume is dedicated to Professor David Elworthy to celebrate his fundamental contribution and exceptional influence on stochastic analysis and related fields. Stochastic analysis has been profoundly developed as a vital fundamental research area in mathematics in recent decades. It has been discovered to have intrinsic connections with many other areas of mathematics such as partial differential equations, functional analysis, topology, differential geometry, dynamical systems, etc. Mathematicians developed many mathematical tools in stochastic analysis to understand and model random phenomena in physics, biology, finance, fluid, environment science, etc. This volume contains 12 comprehensive review/new articles written by world leading researchers (by invitation) and their collaborators. It covers stochastic analysis on manifolds, rough paths, Dirichlet forms, stochastic partial differential equations, stochastic dynamical systems, infinite dimensional analysis, stochastic flows, quantum stochastic analysis and stochastic Hamilton Jacobi theory. Articles contain cutting edge research methodology, results and ideas in relevant fields. They are of interest to research mathematicians and postgraduate students in stochastic analysis, probability, partial differential equations, dynamical systems, mathematical physics, as well as to physicists, financial mathematicians, engineers, etc.

Author : Anonim
Publisher : Unknown
Page : 1260 pages
File Size : 40,5 Mb
Release : 1987
Category : Nuclear energy
ISBN : MINN:319510006497123

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INIS Atomindeks by Anonim Pdf

Author : I. L. Buchbinder,Sergei M. Kuzenko
Publisher : CRC Press
Page : 670 pages
File Size : 50,9 Mb
Release : 1995-02-23
Category : Art
ISBN : UOM:39015047052447

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Ideas and Methods of Supersymmetry and Supergravity, Or a Walk Through Superspace by I. L. Buchbinder,Sergei M. Kuzenko Pdf

This book provides a comprehensive, detailed and self-contained account of four dimensional simple supersymmetry and supergravity. It will be an indispensable source of reference for advanced graduate students, postdoctoral and faculty researchers alike working in quantum field theory, high energy physics, gravity theory, mathematical physics and applied mathematics. The authors develop the subject in its superfield formulation but where appropriate for illustration, analogy and comparison with conventional field theory, they use the component formulation. Throughout the book the authors develop their material in detail with calculation and full discussions of the fundamental ideas and motivations. They discuss many subjects which until now could only be found in the research literature. In addition they present a plethora of new results. The result is the most comprehensive book yet produced on the fundamentals of supersymmetry and supergravity. After studying this book readers should be well prepared to pursue independent research in any area of supersymmetry and supergravity.

Author : Peter G. Bergmann,Venzo De Sabbata
Publisher : Springer
Page : 289 pages
File Size : 42,9 Mb
Release : 2013-12-19
Category : Science
ISBN : 9781489936264

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Topological Properties and Global Structure of Space-Time by Peter G. Bergmann,Venzo De Sabbata Pdf

The Ninth Course of the International School of Cosmology and Gravita tion of the Ettore Majorana Centre for Scientific Culture is concerned with "Topological Properties and Global Structure of Space-Time." We consider this topic to possess great importance. Our choice has also been influenced by the fact that there are many quest ions as yet unre solved. Standard general relativity describes space-time as a four-dimensional pseudo-Riemannian manifold, but it does not prescribe its large-scale structure. Inorderto attempt answers to some topological questions, such as whether our universe is open or closed, whether it is orientable, and whether it is complete or possesses singularities, various theoretical approaches to global aspects of gravitational physics are presented here. As topological questions playa role in non-standard theories as weIl, it will be found that some of the lectures and seminar talks in this volume adopt the point of view of standard relativity, whereas others are based on different theories, such as Kaluza-Klein theories, bimetric theories, and supergravity. We have found it difficult to organize these papers into classes, say standard and non-standard theory, or models with and without singularities. One paper, by R. Reasenberg, is experimental. Its purpose was to give the theorists present an inkling of the opportunities, as weIl as the pitfalls, of experimental research in gravitational physics. Accordingly, we have arranged all contributions alphabetically, by ~first-named) author.

Author : C. Bartocci,U. Bruzzo,Daniel Hernández-Ruipérez
Publisher : Springer Science & Business Media
Page : 255 pages
File Size : 47,8 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.