Download or read book Supersymmetric Gauge Theories in Noncommutative Geometry written by and published by . This book was released on with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Iii iv Provando e riprovando -Accademia del Cimento- In that Empire, the Art of Cartography attained such Perfection that the map of a single Province occupied the entirety of a City, and the map of the Empire, the entirety of a Province. [...] 2.2 M O D U L E S Another important concept that has a central role in what follows is that of a module.2 It can be regarded as a generalization of the notion of a vector space in the sense that the latter is defined over a field whereas the first can be defined over any ring. [...] In cases where it is obvious that we take the tensor product over an algebra instead of over a field, we may drop the reference to the algebra in the notation. [...] (3.24) Since a given Riemannian manifold produces a unique Levi-Civita con- nection and the curvature is derived from that, the latter provides useful information about the manifold: it assigns to every point on the manifold a number that is a measure for the amount of curvature on that point. [...] We can extend the definition of a Clifford algebra to a vector space over the complex numbers by a technique called complexification.

Download or read book Supersymmetry and Noncommutative Geometry written by Wim Beenakker and published by Springer. This book was released on 2015-10-22 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this work the question whether noncommutative geometry allows for supersymmetric theories is addressed. Noncommutative geometry has seen remarkable applications in high energy physics, viz. the geometrical interpretation of the Standard Model, however such a question has not been answered in a conclusive way so far.The book starts with a systematic analysis of the possibilities for so-called almost-commutative geometries on a 4-dimensional, flat background to exhibit not only a particle content that is eligible for supersymmetry, but also have a supersymmetric action. An approach is proposed in which the basic `building blocks' of potentially supersymmetric theories and the demands for their action to be supersymmetric are identified. It is then described how a novel kind of soft supersymmetry breaking Lagrangian arises naturally from the spectral action. Finally, the above formalism is applied to explore the existence of a noncommutative version of the minimal supersymmetric Standard Model.This book is intended for mathematical/theoretical physicists with an interest in the applications of noncommutative geometry to supersymmetric field theories.

Download or read book Geometry of Supersymmetric Gauge Theories written by Francois Gieres and published by Springer. This book was released on 2014-03-12 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph gives a detailed and pedagogical account of the geometry of rigid superspace and supersymmetric Yang-Mills theories. While the core of the text is concerned with the classical theory, the quantization and anomaly problem are briefly discussed following a comprehensive introduction to BRS differential algebras and their field theoretical applications. Among the treated topics are invariant forms and vector fields on superspace, the matrix-representation of the super-Poincaré group, invariant connections on reductive homogeneous spaces and the supermetric approach. Various aspects of the subject are discussed for the first time in textbook and are consistently presented in a unified geometric formalism. Requiring essentially no background on supersymmetry and only a basic knowledge of differential geometry, this text will serve as a mathematically lucid introduction to supersymmetric gauge theories.

Download or read book Geometry of Supersymmetric Gauge Theories Including an Introduction to BRS Differential Algebras and Anomalies written by François Gieres and published by . This book was released on 1988 with total page 189 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Many Faces of the Superworld written by Yuri Golfand and published by World Scientific. This book was released on 2000 with total page 698 pages. Available in PDF, EPUB and Kindle. Book excerpt: This invaluable volume is dedicated to the memory of Yuri Golfand, one of the discoverers of supersymmetry. Together with his student, he constructed in 1970 the superextension of the Poincar‚ algebra and obtained the first four-dimensional supersymmetric field theory, a version of supersymmetric QED. Golfand died in 1994 in Israel.Did the pioneers of supersymmetry ? Neveu, Schwarz, Ramond, Golfand, Volkov, Wess, Zumino and others ? foresee in the early 1970's that they would be opening to us the gates of the superworld? The superworld will become one of the most important components of our understanding of Nature ? a component that will stay with us forever.This book is a compilation of the original papers and review articles, devoted to various aspects of supersymmetry, written by the outstanding researchers in the field, theorists whose work shaped the present day theory and continues to make a profound impact on the frontier directions of the current development. A wide range of topics is covered ? from subtle results in the superstring theory to supersymmetry-based phenomenology. Most of the articles have been prepared specifically for this volume.The first part of the book consists of the Editor's essay presenting the basic stages of Golfand's life and work, the memoirs of his widow, Mrs N Koretz-Golfand and of his student, Dr E Likhtman. Also included is the article of Prof. M Marinov ?Revealing the Path to the Superworld?, outlining the main ideas that paved the way to the discovery of supersymmetry. The historical part of the book concludes with the English translation of the Golfand-Likhtman paper on supersymmetry published in 1972 in the Tamm Memorial Volume.

Download or read book Noncommutative Structures in Mathematics and Physics written by S. Duplij and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Noncommutative Geometry and Physics written by Yoshiaki Maeda and published by World Scientific Publishing Company Incorporated. This book was released on 2005 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonanticommutative harmonic superspace and N = 2 supersymmetric U(l) gauge theory / Takeo Araki, Katsushi Ito and Akihisa Ohtsuka -- Noncommutative locally anti-de sitter black holes / Pierre Bieliavsky ... [et al.] -- Dynamics of fuzzy spaces / M. Burić and John Madore -- Induction of representations in deformation quantization / Henrique Bursztyn and Stefan Waldmann -- [symbol]-function regularization and index theory in noncommutative geometry / Alexander Cardona -- Line bundles on fuzzy CP[symbol] / Ursula Carow-Watamura and Satoshi Watamura -- Construction of Lagrangian embeddings using Hamiltonian actions / River Chiang -- Deformation quantization of complex involutive submanifolds / Andrea D'Agnolo and Pietro Polesello -- Deformation quantization on a Hilbert space / Giuseppe Dito -- Symmetries and Moduli spaces of the self-dual Yang-Mills equations / James D. E. Grant -- Noncommutative solitons and integrable systems / Masashi Hamanaka -- On the connectedness of the spaces of surface group representations / Nan-Kuo Ho and Chiu-Chu Melissa Liu -- Witten's deformed Laplacian and its classical mechanics / Atsushi Inoue -- The vanishing problem for cohomology of superspaces / Daisuke Kato -- Higher dimensional spherical D-branes and matrix model / Yusuke Kimura -- Instantons of [symbol]-models in noncommutative geometry / Giovanni Landi -- On vectorial Gerbes and Poincaré-Cartan classes / Naoya Miyazaki -- A short note on symplectic Floer theory / Kaoru Ono -- Noncommutative cohomological field theories and topological aspects of matrix models / Akifumi Sako -- Gauge theory on fuzzy S[symbol] and CP[symbol] and random matrices / Harold Steinacker -- Relation on spin bundle Gerbes and Mayer's dirac operators / Atsushi Tomoda

Download or read book Noncommutative Geometry And Physics 2005 Proceedings Of The International Sendai beijing Joint Workshop written by Ursula Carow-watamura and published by World Scientific. This book was released on 2007-08-31 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: Noncommutative geometry is a novel approach which is opening up new possibilities for geometry from a mathematical viewpoint. It is also providing new tools for the investigation of quantum space-time in physics. Recent developments in string theory have supported the idea of quantum spaces, and have strongly stimulated the research in this field. This self-contained volume contains survey lectures and research articles which address these issues and related topics. The book is accessible to both researchers and graduate students beginning to study this subject.

Download or read book Noncommutative Geometry And Physics Proceedings Of The Coe International Workshop written by Naoya Miyazaki and published by World Scientific. This book was released on 2005-09-23 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: Noncommutative differential geometry is a novel approach to geometry that is paving the way for exciting new directions in the development of mathematics and physics. The contributions in this volume are based on papers presented at a workshop dedicated to enhancing international cooperation between mathematicians and physicists in various aspects of frontier research on noncommutative differential geometry. The active contributors present both the latest results and comprehensive reviews of topics in the area. The book is accessible to researchers and graduate students interested in a variety of mathematical areas related to noncommutative geometry and its interface with modern theoretical physics.

Download or read book Noncommutative Geometry in M Theory and Conformal Field Theory written by and published by . This book was released on 1999 with total page 171 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the first part of the thesis I will investigate in the Matrix theory framework, the subgroup of dualities of the Discrete Light Cone Quantization of M-theory compactified on tori, which corresponds to T-duality in the auxiliary Type II string theory. After a review of matrix theory compactification leading to noncommutative supersymmetric Yang-Mills gauge theory, I will present solutions for the fundamental and adjoint sections on a two-dimensional twisted quantum torus and generalize to three-dimensional twisted quantum tori. After showing how M-theory T-duality is realized in supersymmetric Yang-Mills gauge theories on dual noncommutative tori I will relate this to the mathematical concept of Morita equivalence of C*-algebras. As a further generalization, I consider arbitrary Ramond-Ramond backgrounds. I will also discuss the spectrum of the toroidally compactified Matrix theory corresponding to quantized electric fluxes on two and three tori. In the second part of the thesis I will present an application to conformal field theory involving quantum groups, another important example of a noncommutative space. First, I will give an introduction to Poisson-Lie groups and arrive at quantum groups using the Feynman path integral. I will quantize the symplectic leaves of the Poisson-Lie group SU(2)*. In this way we obtain the unitary representations of U{sub q}(SU(2)). I discuss the X-structure of SU(2)* and give a detailed description of its leaves using various parametrizations. Then, I will introduce a new reality structure on the Heisenberg double of Fun{sub q} (SL(N, C)) for q phase, which can be interpreted as the quantum phase space of a particle on the q-deformed mass-hyperboloid. I also present evidence that the above real form describes zero modes of certain non-compact WZNW-models.

Download or read book Gauge Theories Applied Supersymmetry And Quantum Gravity Ii Proceedings Of The Workshop written by Alexander Sevrin and published by World Scientific. This book was released on 1997-06-19 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of a meeting held at Imperial College which is devoted to recent developments in string theory, supersymmetry and quantum gravity. The volume comprises two different sections. The first consists of five pedagogical reviews by prominent physicists, covering the currently important subjects of supermembranes, duality, D-branes, new non-perturbative methods and string phenomenology. The second section consists of research reports in these areas and also on other currently important topics such as supersymmetric gauge theories, two-dimensional quantum gravity and black holes.

Download or read book Supersymmetry and Supergravity written by Julius Wess and published by Princeton University Press. This book was released on 2020-05-05 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: This widely acclaimed introduction to N = 1 supersymmetry and supergravity is aimed at readers familiar with relativistic quantum field theory who wish to learn about the supersymmetry algebra. In this new volume Supersymmetry and Supergravity has been greatly expanded to include a detailed derivation of the most general coupling of super-symmetric gauge theory to supergravity. The final result is the starting point for phenomenological studies of supersymmetric theories. The book is distinguished by its pedagogical approach to supersymmetry. It develops several topics in advanced field theory as the need arises. It emphasizes the logical coherence of the subject and should appeal to physicists whose interests range from the mathematical to the phenomenological. In praise of the first edition: "A beautiful exposition of the original ideas of Wess and Zumino in formulating N = 1 supersymmetry and supergravity theories, couched in the language of superfields introduced by Strathdee and the reviewer.... [All] serious students of particle physics would do well to acquire a copy."--Abdus Salam, Nature "An excellent introduction to this exciting area of theoretical physics."--C. J. Isham, Physics Bulletin

Download or read book Gauge Theory on Non anti commutative Superspaces written by Džo Mikulović and published by . This book was released on 2004 with total page 127 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the basic problems of quantum field theories, namely the ultraviolet infinities, is connected to the fact that we consider point particles and spaces which allow the definition of points. The infinities which arise in the gauge theories of the strong and electroweak interactions can be removed by a procedure called renormalization. However, the quantum field theory of gravity is not renormalizable. This is the reason why we say that quantum mechanics and general relativity are not compatible. Although supersymmetry improves its renormalization properties, the theory of supergravity is still not renormalizable. Following the history of unification we could think about circumventing the problem of ultraviolet infinities by dramatically changing spacetime. For example, one could assume that at a sufficiently small fundamental length the spacetime is noncommutative. On such spacetimes the definition of points doesn't make sense. In the present work the author consider gauge theories on non(anti)commutative superspaces. Different construction methods and related problems of these theories are discussed. In particular, the incompatibility of the Seiberg-Witten map with the (anti)chirality, locality and supersymmetry at the same time is demonstrated. Phenomenologically interesting actions are also presented.

Download or read book Quantum Theory Deformation and Integrability written by R. Carroll and published by Elsevier. This book was released on 2000-11-09 with total page 421 pages. Available in PDF, EPUB and Kindle. Book excerpt: About four years ago a prominent string theorist was quoted as saying that it might be possible to understand quantum mechanics by the year 2000. Sometimes new mathematical developments make such understanding appear possible and even close, but on the other hand, increasing lack of experimental verification make it seem to be further distant. In any event one seems to arrive at new revolutions in physics and mathematics every year. This book hopes to convey some of the excitment of this period, but will adopt a relatively pedestrian approach designed to illuminate the relations between quantum and classical. There will be some discussion of philosophical matters such as measurement, uncertainty, decoherence, etc. but philosophy will not be emphasized; generally we want to enjoy the fruits of computation based on the operator formulation of QM and quantum field theory. In Chapter 1 connections of QM to deterministic behavior are exhibited in the trajectory representations of Faraggi-Matone. Chapter 1 also includes a review of KP theory and some preliminary remarks on coherent states, density matrices, etc. and more on deterministic theory. We develop in Chapter 4 relations between quantization and integrability based on Moyal brackets, discretizations, KP, strings and Hirota formulas, and in Chapter 2 we study the QM of embedded curves and surfaces illustrating some QM effects of geometry. Chapter 3 is on quantum integrable systems, quantum groups, and modern deformation quantization. Chapter 5 involves the Whitham equations in various roles mediating between QM and classical behavior. In particular, connections to Seiberg-Witten theory (arising in N = 2 supersymmetric (susy) Yang-Mills (YM) theory) are discussed and we would still like to understand more deeply what is going on. Thus in Chapter 5 we will try to give some conceptual background for susy, gauge theories, renormalization, etc. from both a physical and mathematical point of view. In Chapter 6 we continue the deformation quantization then by exhibiting material based on and related to noncommutative geometry and gauge theory.

Download or read book Topology and Geometry in Physics written by Eike Bick and published by Springer Science & Business Media. This book was released on 2005-01-18 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: Application of the concepts and methods of topology and geometry have led to a deeper understanding of many crucial aspects in condensed matter physics, cosmology, gravity and particle physics. This book can be considered an advanced textbook on modern applications and recent developments in these fields of physical research. Written as a set of largely self-contained extensive lectures, the book gives an introduction to topological concepts in gauge theories, BRST quantization, chiral anomalies, supersymmetric solitons and noncommutative geometry. It will be of benefit to postgraduate students, educating newcomers to the field and lecturers looking for advanced material.

Download or read book Topology and Geometry in Physics written by Eike Bick and published by Springer. This book was released on 2009-09-02 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: Application of the concepts and methods of topology and geometry have led to a deeper understanding of many crucial aspects in condensed matter physics, cosmology, gravity and particle physics. This book can be considered an advanced textbook on modern applications and recent developments in these fields of physical research. Written as a set of largely self-contained extensive lectures, the book gives an introduction to topological concepts in gauge theories, BRST quantization, chiral anomalies, sypersymmetric solitons and noncommutative geometry. It will be of benefit to postgraduate students, educating newcomers to the field and lecturers looking for advanced material.

Download or read book New Dualities of Supersymmetric Gauge Theories written by Jörg Teschner and published by Springer. This book was released on 2015-11-17 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book reviews a number of spectacular advances that have been made in the study of supersymmetric quantum field theories in the last few years. Highlights include exact calculations of Wilson loop expectation values, and highly nontrivial quantitative checks of the long-standing electric-magnetic duality conjectures The book starts with an introductory article presenting a survey of recent advances, aimed at a wide audience with a background and interest in theoretical physics. The following articles are written for advanced students and researchers in quantum field theory, string theory and mathematical physics, our goal being to familiarize these readers with the forefront of current research. The topics covered include recent advances in the classification and vacuum structure of large families of N=2 supersymmetric field theories, followed by an extensive discussion of the localisation method, one of the most powerful tools for exact studies of supersymmetric field theories. The quantities that have been studied in this way are partition functions, expectation values of line operators, and supersymmetric indices. The book also reviews recently discovered connections between SUSY field theories in four dimensions and two-dimensional conformal field theory. These connections have a counterpart in relations between three-dimensional gauge theories and Chern-Simons theory; the book’s closing chapters explore connections with string theory.