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The Green's function method is one of the most powerful and versatile formalisms in physics, and its nonequilibrium version has proved invaluable in many research fields. This book provides a unique, self-contained introduction to nonequilibrium many-body theory. Starting with basic quantum mechanics, the authors introduce the equilibrium and nonequilibrium Green's function formalisms within a unified framework called the contour formalism. The physical content of the contour Green's functions and the diagrammatic expansions are explained with a focus on the time-dependent aspect. Every result is derived step-by-step, critically discussed and then applied to different physical systems, ranging from molecules and nanostructures to metals and insulators. With an abundance of illustrative examples, this accessible book is ideal for graduate students and researchers who are interested in excited state properties of matter and nonequilibrium physics.

Green's functions. --- Many-body problem. --- Quantum theory --- Functions, Green's --- Functions, Induction --- Functions, Source --- Green functions --- Induction functions --- Source functions --- Differential equations --- Potential theory (Mathematics) --- n-body problem --- Problem of many bodies --- Problem of n-bodies --- Mechanics, Analytic --- Mathematics.

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This book is comprehensive in its classical mathematical physics presentation, providing the reader with detailed instructions for obtaining Green's functions from scratch. Green's functions is an instrument easily accessible to practitioners who are engaged in design and exploitation of machines and structures in modern engineering practice. To date, there are no books available on the market that are devoted to the Green's function formalism for equations covered in this volume. The reader, with an undergraduate background in applied mathematics, can become an active user of the Green's function approach. For the first time, Green's functions are discussed for a specific class of problems dealing with potential fields induced in thin-wall structures and therefore, the reader will have first-hand access to a novel issue. This Work is accessible to researchers in applied mathematics, mechanics, and relevant disciplines such as engineering, as well as to upper level undergraduates and graduate students.

Mathematics. --- Differential equations. --- Partial differential equations. --- Numerical analysis. --- Partial Differential Equations. --- Ordinary Differential Equations. --- Classical Mechanics. --- Numerical Analysis. --- Partial differential equations --- 517.91 Differential equations --- Differential equations --- Math --- Science --- Mathematical analysis --- Differential equations, partial. --- Differential Equations. --- Mechanics. --- Classical mechanics --- Newtonian mechanics --- Physics --- Dynamics --- Quantum theory --- Green's functions. --- Functions, Green's --- Functions, Induction --- Functions, Source --- Green functions --- Induction functions --- Source functions --- Potential theory (Mathematics)

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Non-Abelian gauge theories, such as quantum chromodynamics (QCD) or electroweak theory, are best studied with the aid of Green's functions that are gauge-invariant off-shell, but unlike for the photon in quantum electrodynamics, conventional graphical constructions fail. The Pinch Technique provides a systematic framework for constructing such Green's functions, and has many useful applications. Beginning with elementary one-loop examples, this book goes on to extend the method to all orders, showing that the Pinch Technique is equivalent to calculations in the background field Feynman gauge. The Pinch Technique Schwinger-Dyson equations are derived, and used to show how a dynamical gluon mass arises in QCD. Applications are given to the center vortex picture of confinement, the gauge-invariant treatment of resonant amplitudes, the definition of non-Abelian effective charges, high-temperature effects, and even supersymmetry. This book is ideal for elementary particle theorists and graduate students.

Quantum chromodynamics --- Gauge fields (Physics) --- Green's functions. --- Gauge invariance. --- Functions, Green's --- Functions, Induction --- Functions, Source --- Green functions --- Induction functions --- Source functions --- Differential equations --- Potential theory (Mathematics) --- Gage invariance --- Gauge transformations --- Invariance, Gauge --- Electromagnetism --- Symmetry (Physics) --- Transformations (Mathematics) --- Fields, Gauge (Physics) --- Gage fields (Physics) --- Gauge theories (Physics) --- Field theory (Physics) --- Group theory --- Chromodynamics, Quantum --- QCD (Nuclear physics) --- Particles (Nuclear physics) --- Quantum electrodynamics --- Mathematics.

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This book elucidates how Finite Element methods look like from the perspective of Green’s functions, and shows new insights into the mathematical theory of Finite Elements. Practically, this new view on Finite Elements enables the reader to better assess solutions of standard programs and to find better model of a given problem. The book systematically introduces the basic concepts how Finite Elements fulfill the strategy of Green’s functions  and how approximating of Green’s functions. It discusses in detail the discretization error and shows that are coherent with the strategy of “goal oriented refinement”. The book also gives much attention to the dependencies of FE solutions from the parameter set of the model.

Green's functions. --- Quantum theory. --- Green's functions --- Finite element method --- Engineering & Applied Sciences --- Chemical & Materials Engineering --- Physics --- Physical Sciences & Mathematics --- Materials Science --- Applied Mathematics --- Atomic Physics --- Finite element method. --- Engineering. --- Computer mathematics. --- Continuum mechanics. --- Structural mechanics. --- Continuum Mechanics and Mechanics of Materials. --- Computational Mathematics and Numerical Analysis. --- Structural Mechanics. --- Functions, Green's --- Functions, Induction --- Functions, Source --- Green functions --- Induction functions --- Source functions --- Differential equations --- Potential theory (Mathematics) --- FEA (Numerical analysis) --- FEM (Numerical analysis) --- Finite element analysis --- Numerical analysis --- Isogeometric analysis

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Green's functions --- Many-body problem --- Solid state physics --- n-body problem --- Problem of many bodies --- Problem of n-bodies --- Functions, Green's --- Functions, Induction --- Functions, Source --- Green functions --- Induction functions --- Source functions --- Problème des N corps --- Green, Fonctions de --- Physique de l'état solide --- Statistical physics --- Physics --- Solids --- Mechanics, Analytic --- Differential equations --- Potential theory (Mathematics) --- Solid state physics. --- Many-body problem. --- Green's functions. --- Problème des N corps --- Many body problem