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Equilibrium and nonequilibrium properties of correlated many-body systems are of growing interest in many areas of physics, including condensed matter, dense plasmas, nuclear matter and particles. The most powerful and general method which is equally applied to all these areas is given by quantum field theory. This book provides an overview of the basic ideas and concepts of the method of nonequilibrium Green's functions, written by the leading experts and presented in a way accessible to non-specialists and graduate students. It is complemented by invited review papers on modern applications

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)

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Green's functions represent one of the classical and widely used issues in the area of differential equations. This monograph is looking at applied elliptic and parabolic type partial differential equations in two variables. The elliptic type includes the Laplace, static Klein-Gordon and biharmonic equation. The parabolic type is represented by the classical heat equation and the Black-Scholes equation which has emerged as a mathematical model in financial mathematics. The book is attractive for practical needs: It contains many easily computable or computer friendly representations of Green's functions, includes all the standard Green's functions and many novel ones, and provides innovative and new approaches that might lead to Green's functions. The book is a useful source for everyone who is studying or working in the fields of science, finance, or engineering that involve practical solution of partial differential equations.

Green's functions. --- Functions, Green's --- Functions, Induction --- Functions, Source --- Green functions --- Induction functions --- Source functions --- Differential equations --- Potential theory (Mathematics) --- Elliptic. --- Green's Function. --- Parabolic. --- Partial Differential Equation.

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This book presents a functional approach to the construction, use and approximation of Green's functions and their associated ordered exponentials. After a brief historical introduction, the author discusses new solutions to problems involving particle production in crossed laser fields and non-constant electric fields. Applications to problems in potential theory and quantum field theory are covered, along with approximations for the treatment of color fluctuations in high-energy QCD scattering, and a model for summing classes of eikonal graphs in high-energy scattering problems. The book also presents a variant of the Fradkin representation which suggests a new non-perturbative approximation scheme, and provides a qualitative measure of the error involved in each such approximation. Covering the basics as well as more advanced applications, this book is suitable for graduate students and researchers in a wide range of fields, including quantum field theory, fluid dynamics and applied mathematics.

Green's functions. --- Exponential functions. --- Mathematical physics. --- Physical mathematics --- Physics --- Functions, Exponential --- Hyperbolic functions --- Exponents (Algebra) --- Logarithms --- Transcendental functions --- Functions, Green's --- Functions, Induction --- Functions, Source --- Green functions --- Induction functions --- Source functions --- Differential equations --- Potential theory (Mathematics) --- Mathematics

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Mathematical physics --- Solid state physics --- 538.9 --- Physics of condensed matter (in liquid state and solid state) --- Green's functions. --- Mathematics. --- 538.9 Physics of condensed matter (in liquid state and solid state) --- Green's functions --- Physics --- Solids --- Functions, Green's --- Functions, Induction --- Functions, Source --- Green functions --- Induction functions --- Source functions --- Differential equations --- Potential theory (Mathematics) --- Mathematics

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Plasma (Ionized gases) --- Quantum statistics --- Green's functions --- Plasma (Gaz ionisés) --- Statistique quantique --- Green, Fonctions de --- Functions, Green's --- Functions, Induction --- Functions, Source --- Green functions --- Induction functions --- Source functions --- Differential equations --- Potential theory (Mathematics) --- Quantum statistical mechanics --- Matrix mechanics --- Statistical mechanics --- Wave mechanics --- Gaseous discharge --- Gaseous plasma --- Magnetoplasma --- Ionized gases --- Plasma (Gaz ionisés)