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Based on a highly regarded lecture course at Moscow State University, this is a clear and systematic introduction to gauge field theory. It is unique in providing the means to master gauge field theory prior to the advanced study of quantum mechanics. Though gauge field theory is typically included in courses on quantum field theory, many of its ideas and results can be understood at the classical or semi-classical level. Accordingly, this book is organized so that its early chapters require no special knowledge of quantum mechanics. Aspects of gauge field theory relying on quantum mechanics are introduced only later and in a graduated fashion--making the text ideal for students studying gauge field theory and quantum mechanics simultaneously. The book begins with the basic concepts on which gauge field theory is built. It introduces gauge-invariant Lagrangians and describes the spectra of linear perturbations, including perturbations above nontrivial ground states. The second part focuses on the construction and interpretation of classical solutions that exist entirely due to the nonlinearity of field equations: solitons, bounces, instantons, and sphalerons. The third section considers some of the interesting effects that appear due to interactions of fermions with topological scalar and gauge fields. Mathematical digressions and numerous problems are included throughout. An appendix sketches the role of instantons as saddle points of Euclidean functional integral and related topics. Perfectly suited as an advanced undergraduate or beginning graduate text, this book is an excellent starting point for anyone seeking to understand gauge fields.

Gauge fields (Physics) --- Champs de jauge (Physique) --- Gauge fields (Physics). --- Fields, Gauge (Physics) --- Gage fields (Physics) --- Gauge theories (Physics) --- Field theory (Physics) --- Group theory --- Symmetry (Physics)

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By the end of the 1970's, it was clear that all the known forces of nature (including, in a sense, gravity) were examples of gauge theories, characterized by invariance under symmetry transformations chosen independently at each position and each time. These ideas culminated with the finding of the gauge bosons (and perhaps also the Higgs boson). This important book brings together the key papers in the history of gauge theories, including the discoveries of: the role of gauge transformations in the quantum theory of electrically charged particles in the 1920's;

Gauge fields (Physics) --- Field theory (Physics) --- Classical field theory --- Continuum physics --- Physics --- Continuum mechanics --- Fields, Gauge (Physics) --- Gage fields (Physics) --- Gauge theories (Physics) --- Group theory --- Symmetry (Physics)

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Wilson lines (also known as gauge links or eikonal lines) can be introduced in any gauge field theory. Although the concept of the Wilson exponentials finds an enormously wide range of applications in a variety of branches of modern quantum field theory, from condensed matter and lattice simulations to quantum chromodynamics, high-energy effective theories and gravity, there are surprisingly few books or textbooks on the market which contain comprehensive pedagogical introduction and consecutive exposition of the subject. The objective of this book is to get the potential reader acquainted with theoretical and mathematical foundations of the concept of the Wilson loops in the context of modern quantum field theory, to teach him/her to perform independently some elementary calculations with Wilson lines, and to familiarize him/her with the recent development of the subject in different important areas of research. The target audience of the book consists of graduate and postgraduate students working in various areas of quantum field theory, as well as researchers from other fields.

Loops (Group theory) --- Quantum field theory --- Gauge fields (Physics) --- Fields, Gauge (Physics) --- Gage fields (Physics) --- Gauge theories (Physics) --- Field theory (Physics) --- Group theory --- Symmetry (Physics) --- Relativistic quantum field theory --- Quantum theory --- Relativity (Physics) --- Loop groups --- Mathematics.

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"Based on his own work, the author synthesizes the most promising approaches and ideals in field theory today. He presents such subjects as statistical mechanics, quantum field theory and their interrelation, continuous global symmetry, non-Abelian gauge fields, instantons and the quantam theory of loops, and quantum strings and random surfaces. This book is aimed at postgraduate students studying field theory and statistical mechanics, and for research workers in continuous global theory."--Provided by publisher.

Gauge fields (Physics) --- String models --- Champs de jauge (Physique) --- Modèles des cordes vibrantes (Physique nucléaire) --- String models. --- Gauge fields (Physics). --- Modèles des cordes vibrantes (Physique nucléaire) --- Models, String --- String theory --- Nuclear reactions --- Fields, Gauge (Physics) --- Gage fields (Physics) --- Gauge theories (Physics) --- Field theory (Physics) --- Group theory --- Symmetry (Physics) --- A.M. Polyakov --- continuum --- correlation --- function --- invariant --- ising --- limit --- model --- non-abelian --- partition --- theory

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This book addresses several aspects of the integrable structure of the AdS/CFT correspondence. In particular it presents computations made on both sides of the AdS/CFT correspondence, at weak and at strong coupling. On the string theory side of the correspondence, the book focuses on the evaluation of the energy spectrum of closed string solutions moving in some deformed backgrounds that preserve integrability. On the gauge theory side, it explores various formal problems arising in the computation of two and three-point functions by means of the Algebraic Bethe Ansatz and the Quantum Inverse Scattering method. The book features numerous results on integrability in the context of the AdS/CFT correspondence. Self-contained and pedagogical, it includes general discussions and detailed presentations on the use of integrable systems techniques and their applications.

Physics. --- Mathematical physics. --- Quantum field theory. --- String theory. --- Quantum Field Theories, String Theory. --- Mathematical Applications in the Physical Sciences. --- Models, String --- String theory --- Nuclear reactions --- Relativistic quantum field theory --- Field theory (Physics) --- Quantum theory --- Relativity (Physics) --- Physical mathematics --- Physics --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Mathematics --- Gauge fields (Physics) --- Fields, Gauge (Physics) --- Gage fields (Physics) --- Gauge theories (Physics) --- Group theory --- Symmetry (Physics)