Download or read book Function Theory for Higher Spin Equations written by Peter van Lancker and published by Birkhäuser. This book was released on 2016-01-07 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: Examines functions on Rn (rather than spinor-valued functions) with values in the Clifford algebra in higher dimensions Two different methods are presented in parallel for describing function theory for higher spin equations: one based on Clifford analysis, the other on differential geometry For grad students and researchers in analysis, geometry, PDEs, and math physics (electrodynamics, higher spin physics, and string theory)
Download or read book Higher Spin Gauge Theories written by Lars Brink and published by World Scientific. This book was released on 2016-11-01 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: Symmetries play a fundamental role in physics. Non-Abelian gauge symmetries are the symmetries behind theories for massless spin-1 particles, while the reparametrization symmetry is behind Einstein's gravity theory for massless spin-2 particles. In supersymmetric theories these particles can be connected also to massless fermionic particles. Does Nature stop at spin-2 or can there also be massless higher spin theories. In the past strong indications have been given that such theories do not exist. However, in recent times ways to evade those constraints have been found and higher spin gauge theories have been constructed. With the advent of the AdS/CFT duality correspondence even stronger indications have been given that higher spin gauge theories play an important role in fundamental physics.All these issues were discussed at a recent international workshop in Singapore where the leading scientists in the field participated. This volume presents an up-to-date, detailed overview of the theories including its historic background, as well as the latest accomplishments in understanding the foundational properties of higher spin physics.
Download or read book Free Theory written by Anders Bengtsson and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-06-22 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph takes stock of the situation in higher spin gauge theories for the first time. Besides a thorough recapitulation of the field's history, it reviews the progress that has been made and offers a pedagogical introduction to the subject. Abstract approaches to the theory are offered to facilitate a conceptual rethinking of the main problems and to help see patterns hidden by heavy formalism.
Download or read book Introductory Lectures on Higher Spin Theories written by Stefan Fredenhagen and published by Springer Nature. This book was released on with total page 465 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Higher Spin Gauge Theories written by Nicolas Boulanger and published by MDPI. This book was released on 2018-08-09 with total page 459 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a printed edition of the Special Issue "Higher Spin Gauge Theories" that was published in Universe
Download or read book New Frontiers In Fields And Strings Tasi 2015 Proceedings Of The 2015 Theoretical Advanced Study Institute In Elementary Particle Physics written by Joseph Polchinski and published by World Scientific. This book was released on 2016-11-28 with total page 624 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a compilation of lectures delivered at the TASI 2015 summer school, 'New Frontiers in Fields and Strings', held at the University of Colorado Boulder in June 2015. The school focused on topics in theoretical physics of interest to contemporary researchers in quantum field theory and string theory. The lectures are accessible to graduate students in the initial stages of their research careers.
Download or read book A Clifford Analysis Approach to Higher Spin Fields written by Matthias Roels and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Classical Clifford analysis is a generalisation of complex analysis to arbitrary dimension m. At the heart of the theory lies the Dirac operator, a conformally invariant first order differential operator which generalises the role of the Cauchy-Riemann operator. Moreover, the Laplace operator is the square of the Dirac operator, which means that Clifford analysis is a renement of harmonic analysis in m dimensions. While the classical theory is centred around the study of functions taking values in the spinor space, several authors have been studying generalisations of classical Clifford analysis techniques to the so-called higher spin theory. This concerns the study of higher spin operators acting on functions taking values in arbitrary irreducible representations of the spin group. In Clifford analysis, these arbitrary irreducible representations are traditionally defined in terms of polynomial spaces satisfying certain differential equations. From a physical point of view, higher spin fields arise quite naturally: it was shown by Bargmann and Wigner that group theory implies that particles should correspond to irreducible representations of the Lorentz group, labelled by a quantum number called spin. This led to generalisations of the Klein-Gordon and Dirac equation to higher spin equations (Dirac-Fierz-Pauli, Rarita-Schwinger, Buchdahl,...). Although particles with spin higher than one were never detected, a renewed interest in higher spin fields was triggered due to string theory. The reason is that the spectrum of the vibration modes of the strings includes an infinite number of fields of arbitrary increasing spin. With the advent of string theory, one was confronted with the fact that some theories require the space-time to have more than four dimensions. In higher dimensions, new kinds of fields are allowed because more general representations of the Lorentz group exist. In physics, these representations are typically defined as spaces of (traceless) tensors satisfying certain symmetry conditions expressed in terms of Young diagrams. The main goal of this thesis is twofold: in the first part, a proper introduction to Clifford analysis for physicists is given. The second part of this thesis focusses on higher spin fields where we first construct the two-spinor formalism. This is a framework to deal with arbitrary irreducible representations of the double cover of the Lorentz group. Then, this formalism will be linked with the polynomial spaces studied in Clifford analysis. While the two-spinor formalism works only in four dimensions, the polynomial models from Clifford analysis work in arbitrary dimensions and signatures. Finally, higher spin generalisations of the Maxwell equations are studied using techniques from Clifford analysis.
Download or read book String Fields Higher Spins And Number Theory written by Dimitri Polyakov and published by World Scientific. This book was released on 2018-09-18 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book aims to analyze and explore deep and profound relations between string field theory, higher spin gauge theories and holography — the disciplines that have been on the cutting edge of theoretical high energy physics and other fields. These intriguing relations and connections involve some profound ideas in number theory, which appear to be part of a unifying language to describe these connections.
Download or read book Clifford Algebras and their Applications in Mathematical Physics written by F. Brackx and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: This International Conference on Clifford AlgebrfU and Their Application, in Math ematical Phy,ic, is the third in a series of conferences on this theme, which started at the Univer,ity of Kent in Canterbury in 1985 and was continued at the Univer,iU de, Science, et Technique, du Languedoc in Montpellier in 1989. Since the start of this series of Conferences the research fields under consideration have evolved quite a lot. The number of scientific papers on Clifford Algebra, Clifford Analysis and their impact on the modelling of physics phenomena have increased tremendously and several new books on these topics were published. We were very pleased to see old friends back and to wellcome new guests who by their inspiring talks contributed fundamentally to tracing new paths for the future development of this research area. The Conference was organized in Deinze, a small rural town in the vicinity of the University town Gent. It was hosted by De Ceder, a vacation and seminar center in a green area, a typical landscape of Flanders's "plat pays" . The Conference was attended by 61 participants coming from 18 countries; there were 10 main talks on invitation, 37 contributions accepted by the Organizing Com mittee and a poster session. There was also a book display of Kluwer Academic Publishers. As in the Proceedings of the Canterbury and Montpellier conferences we have grouped the papers accordingly to the themes they are related to: Clifford Algebra, Clifford Analysis, Classical Mechanics, Mathematical Physics and Physics Models.
Download or read book Topics in Phase shift Analysis and Higher Spin Field Theory written by Johannes Cornelis Jacobus Maria van Reisen and published by . This book was released on 1983 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Gromov Witten Theory of Spin Curves and Orbifolds written by Tyler Jamison Jarvis and published by American Mathematical Soc.. This book was released on 2006 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a collection of articles on orbifolds, algebraic curves with higher spin structures, and related invariants of Gromov-Witten type. Orbifold Gromov-Witten theory generalizes quantum cohomology for orbifolds, whereas spin cohomological field theory is based on the moduli spaces of higher spin curves and is related by Witten's conjecture to the Gelfand-Dickey integrable hierarchies. A common feature of these two very different looking theories is the central role played by orbicurves in both of them. Insights in one theory can often yield insights into the other. This book brings together for the first time papers related to both sides of this interaction. The articles in the collection cover diverse topics, such as geometry and topology of orbifolds, cohomological field theories, orbifold Gromov-Witten theory, $G$-Frobenius algebra and singularities, Frobenius manifolds and Givental's quantization formalism, moduli of higher spin curves and spin cohomological field theory.
Download or read book Theory of Spinors and Its Application in Physics and Mechanics written by Vladimir A. Zhelnorovich and published by Springer Nature. This book was released on 2019-10-24 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains a systematic exposition of the theory of spinors in finite-dimensional Euclidean and Riemannian spaces. The applications of spinors in field theory and relativistic mechanics of continuous media are considered. The main mathematical part is connected with the study of invariant algebraic and geometric relations between spinors and tensors. The theory of spinors and the methods of the tensor representation of spinors and spinor equations are thoroughly expounded in four-dimensional and three-dimensional spaces. Very useful and important relations are derived that express the derivatives of the spinor fields in terms of the derivatives of various tensor fields. The problems associated with an invariant description of spinors as objects that do not depend on the choice of a coordinate system are addressed in detail. As an application, the author considers an invariant tensor formulation of certain classes of differential spinor equations containing, in particular, the most important spinor equations of field theory and quantum mechanics. Exact solutions of the Einstein–Dirac equations, nonlinear Heisenberg’s spinor equations, and equations for relativistic spin fluids are given. The book presents a large body of factual material and is suited for use as a handbook. It is intended for specialists in theoretical physics, as well as for students and post-graduate students of physical and mathematical specialties.
Download or read book 3 D Spinors Spin Weighted Functions and their Applications written by Gerardo F. Torres del Castillo and published by Springer Science & Business Media. This book was released on 2003-07-25 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book on the theory of three-dimensional spinors and their applications fills an important gap in the literature. It gives an introductory treatment of spinors. From the reviews: "Gathers much of what can be done with 3-D spinors in an easy-to-read, self-contained form designed for applications that will supplement many available spinor treatments. The book...should be appealing to graduate students and researchers in relativity and mathematical physics." -—MATHEMATICAL REVIEWS
Download or read book Nuclear Science Abstracts written by and published by . This book was released on 1976 with total page 964 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Topics in Clifford Analysis written by Swanhild Bernstein and published by Springer Nature. This book was released on 2019-10-15 with total page 503 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quaternionic and Clifford analysis are an extension of complex analysis into higher dimensions. The unique starting point of Wolfgang Sprößig’s work was the application of quaternionic analysis to elliptic differential equations and boundary value problems. Over the years, Clifford analysis has become a broad-based theory with a variety of applications both inside and outside of mathematics, such as higher-dimensional function theory, algebraic structures, generalized polynomials, applications of elliptic boundary value problems, wavelets, image processing, numerical and discrete analysis. The aim of this volume is to provide an essential overview of modern topics in Clifford analysis, presented by specialists in the field, and to honor the valued contributions to Clifford analysis made by Wolfgang Sprößig throughout his career.
Download or read book Relativistic Quantum Mechanics written by Walter Greiner and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: Relativistic Quantum Mechanics - Wave Equations concentrates mainly on the wave equations for spin-0 and spin-1/2 particles. Chapter 1 deals with the Klein-Gordon equation and its properties and applications. The chapters that follow introduce the Dirac equation, investigate its covariance properties and present various approaches to obtaining solutions. Numerous applications are discussed in detail, including the two-center Dirac equation, hole theory, CPT symmetry, Klein's paradox, and relativistic symmetry principles. Chapter 15 presents the relativistic wave equations for higher spin (Proca, Rarita-Schwinger, and Bargmann-Wigner). The extensive presentation of the mathematical tools and the 62 worked examples and problems make this a unique text for an advanced quantum mechanics course.
Download or read book Handbook of Functional Equations written by Themistocles M. Rassias and published by Springer. This book was released on 2014-11-21 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: This handbook consists of seventeen chapters written by eminent scientists from the international mathematical community, who present important research works in the field of mathematical analysis and related subjects, particularly in the Ulam stability theory of functional equations. The book provides an insight into a large domain of research with emphasis to the discussion of several theories, methods and problems in approximation theory, analytic inequalities, functional analysis, computational algebra and applications. The notion of stability of functional equations has its origins with S. M. Ulam, who posed the fundamental problem for approximate homomorphisms in 1940 and with D. H. Hyers, Th. M. Rassias, who provided the first significant solutions for additive and linear mappings in 1941 and 1978, respectively. During the last decade the notion of stability of functional equations has evolved into a very active domain of mathematical research with several applications of interdisciplinary nature. The chapters of this handbook focus mainly on both old and recent developments on the equation of homomorphism for square symmetric groupoids, the linear and polynomial functional equations in a single variable, the Drygas functional equation on amenable semigroups, monomial functional equation, the Cauchy–Jensen type mappings, differential equations and differential operators, operational equations and inclusions, generalized module left higher derivations, selections of set-valued mappings, D’Alembert’s functional equation, characterizations of information measures, functional equations in restricted domains, as well as generalized functional stability and fixed point theory.
