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Author: Gerald Dunne Publisher: Springer Science & Business Media ISBN: 3540447776 Category : Science Languages : en Pages : 226
Book Description
Self-duality greatly reduces the mathematical difficulties of a theory but it is also a notion of considerable physical significance. The new class of self-dual Chern-Simons theories discussed in detail in this book arise in the context of anyonic quantum field theory and have applications to models such as the quantum Hall effect, anyonic superconductivity, and Aharonov-Bohm scattering. There are also interesting connections with the theory of integrable models. The author presents the abelian and non-abelian models for relativistic and non-relativistic realizations of the self-dual Chern-Simons theories and finishes with some applications in quantum physics. The book is written for advanced students and researchers in mathematical, particle, and condensed matter physics.
Author: Gerald Dunne Publisher: Springer Science & Business Media ISBN: 3540447776 Category : Science Languages : en Pages : 226
Book Description
Self-duality greatly reduces the mathematical difficulties of a theory but it is also a notion of considerable physical significance. The new class of self-dual Chern-Simons theories discussed in detail in this book arise in the context of anyonic quantum field theory and have applications to models such as the quantum Hall effect, anyonic superconductivity, and Aharonov-Bohm scattering. There are also interesting connections with the theory of integrable models. The author presents the abelian and non-abelian models for relativistic and non-relativistic realizations of the self-dual Chern-Simons theories and finishes with some applications in quantum physics. The book is written for advanced students and researchers in mathematical, particle, and condensed matter physics.
Author: Gabriella Tarantello Publisher: Springer Science & Business Media ISBN: 0817646086 Category : Science Languages : en Pages : 335
Book Description
This monograph discusses specific examples of selfdual gauge field structures, including the Chern–Simons model, the abelian–Higgs model, and Yang–Mills gauge field theory. The author builds a foundation for gauge theory and selfdual vortices by introducing the basic mathematical language of gauge theory and formulating examples of Chern–Simons–Higgs theories (in both abelian and non-abelian settings). Thereafter, the Electroweak theory and self-gravitating Electroweak strings are examined. The final chapters treat elliptic problems involving Chern–Simmons models, concentration-compactness principles, and Maxwell–Chern–Simons vortices.
Author: Haim Brzis Publisher: World Scientific ISBN: 9812382623 Category : Mathematics Languages : en Pages : 302
Book Description
ICM 2002 Satellite Conference on Nonlinear Analysis was held in the period: August 1418, 2002 at Taiyuan, Shanxi Province, China. This conference was organized by Mathematical School of Peking University, Academy of Mathematics and System Sciences of Chinese Academy of Sciences, Mathematical school of Nankai University, and Department of Mathematics of Shanxi University, and was sponsored by Shanxi Province Education Committee, Tian Yuan Mathematics Foundation, and Shanxi University. 166 mathematicians from 21 countries and areas in the world attended the conference. 53 invited speakers and 30 contributors presented their lectures. This conference aims at an overview of the recent development in nonlinear analysis. It covers the following topics: variational methods, topological methods, fixed point theory, bifurcations, nonlinear spectral theory, nonlinear Schrvdinger equations, semilinear elliptic equations, Hamiltonian systems, central configuration in N-body problems and variational problems arising in geometry and physics.
Author: Henri Berestycki Publisher: Springer Science & Business Media ISBN: 9401003076 Category : Mathematics Languages : en Pages : 525
Book Description
Nonlinear partial differential equations abound in modern physics. The problems arising in these fields lead to fascinating questions and, at the same time, progress in understanding the mathematical structures is of great importance to the models. Nevertheless, activity in one of the approaches is not always sufficiently in touch with developments in the other field. The book presents the joint efforts of mathematicians and physicists involved in modelling reactive flows, in particular superconductivity and superfluidity. Certain contributions are fundamental to an understanding of such cutting-edge research topics as rotating Bose-Einstein condensates, Kolmogorov-Zakharov solutions for weak turbulence equations, and the propagation of fronts in heterogeneous media.
Author: Vladimir G. Turaev Publisher: European Mathematical Society ISBN: 9783037190869 Category : Mathematics Languages : en Pages : 300
Book Description
Homotopy Quantum Field Theory (HQFT) is a branch of Topological Quantum Field Theory founded by E. Witten and M. Atiyah. It applies ideas from theoretical physics to study principal bundles over manifolds and, more generally, homotopy classes of maps from manifolds to a fixed target space. This book is the first systematic exposition of Homotopy Quantum Field Theory. It starts with a formal definition of an HQFT and provides examples of HQFTs in all dimensions. The main body of the text is focused on $2$-dimensional and $3$-dimensional HQFTs. A study of these HQFTs leads to new algebraic objects: crossed Frobenius group-algebras, crossed ribbon group-categories, and Hopf group-coalgebras. These notions and their connections with HQFTs are discussed in detail. The text ends with several appendices including an outline of recent developments and a list of open problems. Three appendices by M. Muger and A. Virelizier summarize their work in this area. The book is addressed to mathematicians, theoretical physicists, and graduate students interested in topological aspects of quantum field theory. The exposition is self-contained and well suited for a one-semester graduate course. Prerequisites include only basics of algebra and topology.
Author: Raoul Bott Publisher: Springer Science & Business Media ISBN: 1475739516 Category : Mathematics Languages : en Pages : 319
Book Description
Developed from a first-year graduate course in algebraic topology, this text is an informal introduction to some of the main ideas of contemporary homotopy and cohomology theory. The materials are structured around four core areas: de Rham theory, the Cech-de Rham complex, spectral sequences, and characteristic classes. By using the de Rham theory of differential forms as a prototype of cohomology, the machineries of algebraic topology are made easier to assimilate. With its stress on concreteness, motivation, and readability, this book is equally suitable for self-study and as a one-semester course in topology.
Author: Sam Treiman Publisher: Princeton University Press ISBN: 1400854563 Category : Science Languages : en Pages : 550
Book Description
Current algebra remains our most successful analysis of fundamental particle interactions. This collection of surveys on current algebra and anomalies is a successor volume to Lectures on Current Algebra and Its Applications (Princeton Series in Physics, 1972). Originally published in 1986. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Author: Gerald Dunne
Author: Gerald Dunne
Author: Gabriella Tarantello
Author: Gerald Dunne
Author: Kihyun Kim
Author: A. Comtet
Author: Haim Brzis
Author: Henri Berestycki
Author: Vladimir G. Turaev
Author: Raoul Bott
Author: Sam Treiman