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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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This volume is devoted to different facets of QCD, stressing non-perturbative, analytic and lattice formulations, scattering solutions and approximations, and the understanding of recent RHIC experiments. It discusses ideas of the fifth dimension, originating in brane theory, as well as possible experimental tests and predictions of those ideas.

Quantum chromodynamics --- Quantum field theory --- Scattering (Physics) --- Perturbation (Quantum dynamics) --- Perturbation theory, Quantum mechanical --- Perturbation (Mathematics) --- Quantum theory --- Congresses --- Quantum chromodynamics - Congresses