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Author : Roberto Percacci
Publisher : World Scientific
ISBN 13 : 9813104244
Total Pages : 267 pages
Book Rating : 4.8/5 (131 download)
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:
Author : Roberto Percacci
Publisher : World Scientific Publishing Company Incorporated
ISBN 13 : 9789971500795
Total Pages : 255 pages
Book Rating : 4.5/5 (7 download)
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.
Author : Robert Hermann
Publisher : Math Science Press
ISBN 13 : 9780915692422
Total Pages : 363 pages
Book Rating : 4.6/5 (924 download)
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.
Author : Ernst Binz
Publisher : Courier Corporation
ISBN 13 : 0486150445
Total Pages : 474 pages
Book Rating : 4.4/5 (861 download)
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.
Author : Robert Hermann
Publisher :
ISBN 13 : 9780915692293
Total Pages : 610 pages
Book Rating : 4.6/5 (922 download)
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:
Author : Yuri I. Manin
Publisher : Springer Science & Business Media
ISBN 13 : 9783540613787
Total Pages : 368 pages
Book Rating : 4.6/5 (137 download)
Download or read book Gauge Field Theory and Complex Geometry written by Yuri I. Manin and published by Springer Science & Business Media. This book was released on 1997-05-20 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "... focused mainly on complex differential geometry and holomorphic bundle theory. This is a powerful book, written by a very distinguished contributor to the field" (Contemporary Physics )"the book provides a large amount of background for current research across a spectrum of field. ... requires effort to read but it is worthwhile and rewarding" (New Zealand Math. Soc. Newsletter) " The contents are highly technical and the pace of the exposition is quite fast. Manin is an outstanding mathematician, and writer as well, perfectly at ease in the most abstract and complex situation. With such a guide the reader will be generously rewarded!" (Physicalia) This new edition includes an Appendix on developments of the last 10 years, by S. Merkulov.
Author : Supriya Kar
Publisher : World Scientific Publishing Company Incorporated
ISBN 13 : 9789812380524
Total Pages : 250 pages
Book Rating : 4.3/5 (85 download)
Download or read book Non-commutative Geometry written by Supriya Kar and published by World Scientific Publishing Company Incorporated. This book was released on 2018-01-31 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a systematic, comprehensive and up-to-date account of the recent developments in non-commutative geometry, at a pedagogical level. It does not go into the details of rigorous (advanced level) mathematical formulation of non-commutative geometry; rather, it restricts itself to the domain of strings and quantum fields.Since non-commutative geometry has recently aroused renewed interest in open string theory, the author motivates the text from the viewpoint of a string theory. He begins with an introduction to the subject, explaining what one means by non-commutative geometry and why it is relevant to study such geometry, and discussing its possible origin in a string theory.The book comprises nine chapters. Chapter 1 gives a sound mathematical ntroduction to non-commutative spacetime coordinates in classical and quantum physics. In Chapter 2, non-commutativity in a string theory is discussed at a pedagogic level. Chapter 3 deals with an aribitrary D-brane dynamics and Chapter 4 describes the non-commutative gauge theories on a D-brane. In Chapters 5-9, non-commutative quantum field theory (NCQFT) is addressed. In particular, Chapter 5 deals with the real scalar NCQFT, Chapter 6 with that of complex scalar field, Chapter 7 describes spontaneous symmetry breaking in scalar NCQFT, Chapter 8 deals with the U(1) Gauge theory and Chapter 9 with SU(n) Gauge theories.Students will find this book useful as a bridge between string and field theories. In addition, it will prove invaluable for interdisciplinary areas of study.
Author : S. de Filippo
Publisher : Elsevier
ISBN 13 : 0444598715
Total Pages : 259 pages
Book Rating : 4.4/5 (445 download)
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.
Author : Sergei V. Ketov
Publisher : Springer Science & Business Media
ISBN 13 : 3662041928
Total Pages : 429 pages
Book Rating : 4.6/5 (62 download)
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.
Author : Peter Breitenlohner
Publisher : Springer
ISBN 13 : 9783662136669
Total Pages : 242 pages
Book Rating : 4.1/5 (366 download)
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.
Author : Daniel S. Freed
Publisher : American Mathematical Soc.
ISBN 13 : 0821804006
Total Pages : 472 pages
Book Rating : 4.8/5 (218 download)
Download or read book Geometry and Quantum Field Theory written by Daniel S. Freed and published by American Mathematical Soc.. This book was released on 1995 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: Exploring topics from classical and quantum mechnanics and field theory, this book is based on lectures presented in the Graduate Summer School at the Regional Geometry Institute in Park City, Utah, in 1991. The chapter by Bryant treats Lie groups and symplectic geometry, examining not only the connection with mechanics but also the application to differential equations and the recent work of the Gromov school. Rabin's discussion of quantum mechanics and field theory is specifically aimed at mathematicians. Alvarez describes the application of supersymmetry to prove the Atiyah-Singer index theorem, touching on ideas that also underlie more complicated applications of supersymmetry. Quinn's account of the topological quantum field theory captures the formal aspects of the path integral and shows how these ideas can influence branches of mathematics which at first glance may not seem connected. Presenting material at a level between that of textbooks and research papers, much of the book would provide excellent material for graduate courses. The book provides an entree into a field that promises to remain exciting and important for years to come.
Author : Garth Baker
Publisher : Birkhäuser
ISBN 13 : 3034888953
Total Pages : 166 pages
Book Rating : 4.0/5 (348 download)
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.
Author : Yuri I. Manin
Publisher : Springer Science & Business Media
ISBN 13 : 3662073862
Total Pages : 357 pages
Book Rating : 4.6/5 (62 download)
Download or read book Gauge Field Theory and Complex Geometry written by Yuri I. Manin and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "... focused mainly on complex differential geometry and holomorphic bundle theory. This is a powerful book, written by a very distinguished contributor to the field" (Contemporary Physics )"the book provides a large amount of background for current research across a spectrum of field. ... requires effort to read but it is worthwhile and rewarding" (New Zealand Math. Soc. Newsletter) " The contents are highly technical and the pace of the exposition is quite fast. Manin is an outstanding mathematician, and writer as well, perfectly at ease in the most abstract and complex situation. With such a guide the reader will be generously rewarded!" (Physicalia) This new edition includes an Appendix on developments of the last 10 years, by S. Merkulov.
Author : C. Truesdell
Publisher : Springer Science & Business Media
ISBN 13 : 3662131838
Total Pages : 600 pages
Book Rating : 4.6/5 (621 download)
Download or read book The Non-Linear Field Theories of Mechanics written by C. Truesdell and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 600 pages. Available in PDF, EPUB and Kindle. Book excerpt: This third edition includes the corrections made by the late C. Truesdell in his personal copy. It is annotated by S. Antman who describes the monograph`s genesis and the impact it has made on the modern development of mechanics. Originally published as Volume III/3 of the famous Encyclopedia of Physics in 1965, this book describes and summarizes "everything that was both known and worth knowing in the field at the time." It also has greatly contributed to the unification and standardization of the concepts, terms and notations in the field.
Author : Manuel de León
Publisher : World Scientific
ISBN 13 : 9814699772
Total Pages : 220 pages
Book Rating : 4.8/5 (146 download)
Download or read book Methods of Differential Geometry in Classical Field Theories written by Manuel de León and published by World Scientific. This book was released on 2015-10-21 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to review two of the most relevant approaches to the study of classical field theories of the first order, say k-symplectic and k-cosymplectic geometry. This approach is also compared with others like multisymplectic formalism. It will be very useful for researchers working in classical field theories and graduate students interested in developing a scientific career in the subject. Contents:A Review of Hamiltonian and Lagrangian Mechanics:Hamiltonian and Lagrangian Mechanicsk-Symplectic Formulation of Classical Field Theories:k-Symplectic Geometryk-Symplectic FormalismHamiltonian Classical Field TheoryHamilton–Jacobi Theory in k-Symplectic Field TheoriesLagrangian Classical Field TheoriesExamplesk-Cosymplectic Formulation of Classical Field Theories:k-Cosymplectic Geometryk-Cosymplectic FormalismHamiltonian Classical Field TheoriesHamilton–Jacobi EquationLagrangian Classical Field TheoriesExamplesk-Symplectic Systems versus Autonomous k-Cosymplectic SystemsRelationship between k-Symplectic and k-Cosymplectic Approaches and the Multisymplectic Formalism:Multisymplectic FormalismAppendices:Symplectic ManifoldsCosymplectic ManifoldsGlossary of Symbols Readership: Graduate students and researchers in classical field theories. Key Features:This book contains for the first time this new geometric approach to Classical Field Theory. Up to now the theory is disseminated in several journal papersThe subject is very active in the last yearsThere are many open problems in Classical Field Theories to be attacked using this new formalismKeywords:Classical Field Theory;k-Symplectic;k-Cosymplectic;Multisymplectic Formalism
Author : P. Bandyopadhyay
Publisher : Springer Science & Business Media
ISBN 13 : 9401716978
Total Pages : 225 pages
Book Rating : 4.4/5 (17 download)
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.
Author : Alexander Cardona
Publisher : World Scientific
ISBN 13 : 9814487678
Total Pages : 492 pages
Book Rating : 4.8/5 (144 download)
Download or read book Geometric and Topological Methods for Quantum Field Theory written by Alexander Cardona and published by World Scientific. This book was released on 2003-03-21 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume offers an introduction to recent developments in several active topics of research at the interface between geometry, topology and quantum field theory. These include Hopf algebras underlying renormalization schemes in quantum field theory, noncommutative geometry with applications to index theory on one hand and the study of aperiodic solids on the other, geometry and topology of low dimensional manifolds with applications to topological field theory, Chern-Simons supergravity and the anti de Sitter/conformal field theory correspondence. It comprises seven lectures organized around three main topics, noncommutative geometry, topological field theory, followed by supergravity and string theory, complemented by some short communications by young participants of the school. Contents:Noncommutative Geometry:Hopf Algebras in Noncommutative Geometry (J C Várilly)The Noncommutative Geometry of Aperiodic Solids (J Bellissard)Noncommutative Geometry and Abstract Integration Theory (M-T Benameur)Topological Field Theory:Introduction to Quantum Invariants of 3-Manifolds, Topological Quantum Field Theories and Modular Categories (C Blanchet)An Introduction to Donaldson–Witten Theory (M Mariño)Supergravity and String Theory:(Super)-Gravities Beyond 4 Dimensions (J Zanelli)Introductory Lectures on String Theory and the AdS/CFT Correspondence (A Pankiewicz & S Theisen)Short Communications:Group Contractions and Its Consequences Upon Representations of Different Spatial Symmetry Groups (M Ayala-Sánchez & R W Haase)Phase Anomalies as Trace Anomalies in Chern–Simons Theory (A Cardona)Deligne Cohomology for Orbifolds, Discrete Torsion and B-Fields (E Lupercio & B Uribe) Readership: Graduate students and researchers in theoretical and mathematical physics, as well as geometry and topology. Keywords:
