Download or read book Geometry of Nonlinear Field Theories written by Roberto Percacci and published by World Scientific. This book was released on with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Geometry of Nonlinear Field Theories written by Roberto Percacci and published by World Scientific Publishing Company Incorporated. This book was released on 1986 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses the deep connection between gravitation and the nonlinear sigma model coupled to gauge fields in a new perspective. Interesting developments emerge. Some other new aspects are provided such as the constant use of infinite dimensional differential geometry, a powerful tool not only for making the theory more rigorous but also for a heuristic understanding of field theory. A systematic treatment of the topological properties of Yang-Mills theory, the nonlinear sigma model and gravity is also given. Being sufficiently pedagogical and self-contained, this book could also be used as a base for an interdisciplinary course at the graduate level.
Download or read book Twistor Geometry and Field Theory written by R. S. Ward and published by Cambridge University Press. This book was released on 1990 with total page 534 pages. Available in PDF, EPUB and Kindle. Book excerpt: Deals with the twistor treatment of certain linear and non-linear partial differential equations. The description in terms of twistors involves algebraic and differential geometry, and several complex variables.
Download or read book Twistor Geometry and Non Linear Systems written by H.D. Doebner and published by Springer. This book was released on 2006-11-14 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Geometric Structures in Nonlinear Physics written by Robert Hermann and published by Math Science Press. This book was released on 1991 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: VOLUME 26 of INTERDISCIPLINARY MATHEMATICS, series expounding mathematical methodology in Physics & Engineering. TOPICS: Differential & Riemannian Geometry; Theories of Vorticity Dynamics, Einstein-Hilbert Gravitation, Colobeau-Rosinger Generalized Function Algebra, Deformations & Quantum Mechanics of Particles & Fields. Ultimate goal is to develop mathematical framework for reconciling Quantum Mechanics & concept of Point Particle. New ideas for researchers & students. Order: Math Sci Press, 53 Jordan Road, Brookline, MA 02146. (617) 738-0307.
Download or read book Cartanian Geometry Nonlinear Waves and Control Theory written by Robert Hermann and published by . This book was released on 1979 with total page 610 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Geometry of Classical Fields written by Ernst Binz and published by Courier Corporation. This book was released on 2011-11-30 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: A canonical quantization approach to classical field theory, this text is suitable for mathematicians interested in theoretical physics as well as to theoretical physicists who use differential geometric methods in their modelling. Introduces differential geometry, the theory of Lie groups, and progresses to discuss the systematic development of a covariant Hamiltonian formulation of field theory. 1988 edition.
Download or read book Geometrical and Algebraic Aspects of Nonlinear Field Theory written by S. de Filippo and published by Elsevier. This book was released on 2012-12-02 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: Experts in general relativity, particle physics and mathematical physics discuss aspects of their recent research. The main emphasis is on the geometrical and algebraic methods used in solving a wide range of problems.
Download or read book Quantum Non linear Sigma Models written by Sergei V. Ketov and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 429 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first comprehensive presentation of the quantum non-linear sigma-models. The original papers consider in detail geometrical properties and renormalization of a generic non-linear sigma-model, illustrated by explicit multi-loop calculations in perturbation theory.
Download or read book Renormalization of Quantum Field Theories with Non linear Field Transformations written by Peter Breitenlohner and published by Springer. This book was released on 2014-03-12 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: The characteristic feature of many models for field theories based on concepts of differential geometry is their nonlinearity. In this book a systematic exposition of nonlinear transformations in quantum field theory is given. The book starts with a short account of the renormalization theory with examples which can be handled successfully in four space-time dimensions. The second part is devoted to nonlinear sigma-models and their constructions in two dimensions. In the final section geometrical and cohomological methods and the relations to string theory are treated. This book is an important contribution towards rigorous definitions, and the mastering of nonlinear reparametrizations in agreement with the principles of quantum field theory will help to deal with anomalies, geometry and the like consistently and thus to understand better their implications for physics. The collection of papers addresses researchers and graduate students as well and will stimulate further work on the foundations of quantum field theory.
Download or read book Nonlinear Partial Differential Equations in Geometry and Physics written by Garth Baker and published by Birkhäuser. This book was released on 2012-12-06 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the proceedings of a series of lectures hosted by the Math ematics Department of The University of Tennessee, Knoxville, March 22-24, 1995, under the title "Nonlinear Partial Differential Equations in Geometry and Physics" . While the relevance of partial differential equations to problems in differen tial geometry has been recognized since the early days of the latter subject, the idea that differential equations of differential-geometric origin can be useful in the formulation of physical theories is a much more recent one. Perhaps the earliest emergence of systems of nonlinear partial differential equations having deep geo metric and physical importance were the Einstein equations of general relativity (1915). Several basic aspects of the initial value problem for the Einstein equa tions, such as existence, regularity and stability of solutions remain prime research areas today. eighty years after Einstein's work. An even more recent development is the realization that structures originally the context of models in theoretical physics may turn out to have introduced in important geometric or topological applications. Perhaps its emergence can be traced back to 1954, with the introduction of a non-abelian version of Maxwell's equations as a model in elementary-particle physics, by the physicists C.N. Yang and R. Mills. The rich geometric structure ofthe Yang-Mills equations was brought to the attention of mathematicians through work of M.F. Atiyah, :"J. Hitchin, I.
Download or read book Gauge Field Theory and Complex Geometry written by I︠U︡. I. Manin and published by Springer. This book was released on 1988-06-28 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: "In the last two decades two new ideas were introduced into mathematical physics. The first of these is the notion of twistor geometry and the other that of supersymmetry. In this book by Y.I. Manin we find a beautiful blend of developments stemming from these two ideas written by a master expositor who uses the language of algebraic geometry to synthesize and unify the fundamental ideas involves." From a review of the Russian edition#1 The exposition is geometrized and unified. Applications to the solution of nonlinear differential equations of quantum field theory are given, in particular to the theory of instantons. The second part of the book contains a mathematical introduction to superalgebra and supergeometry which can be read independently and used by students in algebra and geometry. For the first time in the mathematical literature an introduction to the geometry of supergravity is given. Methods of complex geometry, in particular sheaf cohomology, are used throughout. Since the newest quantum field theory, dealing with (super)unification schemes and (super)strings uses more and more of complex geometry, this book may serve to introduce both physicists and mathematicians to this quickly expanding domain.
Download or read book Geometry Topology and Quantum Field Theory written by P. Bandyopadhyay and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a monograph on geometrical and topological features which arise in quantum field theory. It is well known that when a chiral fermion interacts with a gauge field we have chiral anomaly which corresponds to the fact that divergence of the axial vector current does not vanish. It is observed that this is related to certain topological features associated with the fermion and leads to the realization of the topological origin of fermion number as well as the Berry phase. The role of gauge fields in the quantization procedure has its implications in these topological features of a fermion and helps us to consider a massive fermion as a soliton (skyrrnion). In this formalism chiral anomaly is found to be responsible for mass generation. This has its relevance in electroweak theory where it is observed that weak interaction gauge bosons attain mass topologically. The geometrical feature of a skyrmion also helps us to realize the internal symmetry of hadrons from reflection group. Finally it has been shown that noncommutative geometry where the space time manifold is taken to be X = M x Zz has its relevance in the description of a massive 4 fermion as a skyrmion when the discrete space is considered as the internal space and the symmetry breaking leads to chiral anomaly. In chap. l preliminary mathematical formulations related to the spinor structure have been discussed. In chap.
Download or read book Renormalization of Quantum Field Theories with Non linear Field Transformations written by Peter Breitenlohner and published by Springer Verlag. This book was released on 1988 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The characteristic feature of many models for field theories based on concepts of differential geometry is their nonlinearity. In this book a systematic exposition of nonlinear transformations in quantum field theory is given. The book starts with a short account of the renormalization theory with examples which can be handled successfully in four space-time dimensions. The second part is devoted to nonlinear sigma-models and their constructions in two dimensions. In the final section geometrical and cohomological methods and the relations to string theory are treated. This book is an important contribution towards rigorous definitions, and the mastering of nonlinear reparametrizations in agreement with the principles of quantum field theory will help to deal with anomalies, geometry and the like consistently and thus to understand better their implications for physics. The collection of papers addresses researchers and graduate students as well and will stimulate further work on the foundations of quantum field theory.
Download or read book Geometry and Theoretical Physics written by Joachim Debrus and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: The interaction between geometry and theoretical physics has often been very fruitful. A highlight in this century was Einstein's creation of the theory of general relativity. Equally impressive was the recognition, starting from the work of Yang and Mills and culminating in the Weinberg-Salam theory of the electroweak interaction and quantum chromodynamics, that the fundamental interactions of elementary particles are governed by gauge fields, which in ma thematical terms are connections in principal fibre bundles. Theoretical physi cists became increasingly aware of the fact that the use of modern mathematical methods may be necessary in the treatment of problems of physical interest. Since some of these topics are covered at most summarily in the usual curricu lum, there is a need for extra-curricular efforts to provide an opportunity for learning these techniques and their physical applications. In this context we arranged a meeting at the Physikzentrum Bad Ronnef 12-16 February 1990 on the subject "Geometry and Theoretical Physics", in the series of physics schools organized by the German Physical Society. The participants were graduate students from German universities and research institutes. Since the meeting occurred only a short time after freedom of travel between East and West Germany became a reality, this was for many from the East the first opportunity to attend a scientific meeting in the West, and for many from the West the first chance to become personally acquainted with colleagues from the East.
Download or read book Connections In Classical And Quantum Field Theory written by Luigi Mangiarotti and published by World Scientific. This book was released on 2000-04-28 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometrical notions and methods play an important role in both classical and quantum field theory, and a connection is a deep structure which apparently underlies the gauge-theoretical models in field theory and mechanics. This book is an encyclopaedia of modern geometric methods in theoretical physics. It collects together the basic mathematical facts about various types of connections, and provides a detailed exposition of relevant physical applications. It discusses the modern issues concerning the gauge theories of fundamental fields. The authors have tried to give all the necessary mathematical background, thus making the book self-contained.This book should be useful to graduate students, physicists and mathematicians who are interested in the issue of deep interrelations between theoretical physics and geometry.
Download or read book Geometry of Harmonic Maps written by Yuanlong Xin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: Harmonic maps are solutions to a natural geometrical variational prob lem. This notion grew out of essential notions in differential geometry, such as geodesics, minimal surfaces and harmonic functions. Harmonic maps are also closely related to holomorphic maps in several complex variables, to the theory of stochastic processes, to nonlinear field theory in theoretical physics, and to the theory of liquid crystals in materials science. During the past thirty years this subject has been developed extensively. The monograph is by no means intended to give a complete description of the theory of harmonic maps. For example, the book excludes a large part of the theory of harmonic maps from 2-dimensional domains, where the methods are quite different from those discussed here. The first chapter consists of introductory material. Several equivalent definitions of harmonic maps are described, and interesting examples are presented. Various important properties and formulas are derived. Among them are Bochner-type formula for the energy density and the second varia tional formula. This chapter serves not only as a basis for the later chapters, but also as a brief introduction to the theory. Chapter 2 is devoted to the conservation law of harmonic maps. Em phasis is placed on applications of conservation law to the mono tonicity formula and Liouville-type theorems.
