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"This book is directed toward readers who are interested in learning about the Newtonian N-body problem, as well as toward students and experts in this area who are interested in new expositions of past results, previously unpublished research conclusions, and new research problems. As many readers will have no previous knowledge about this fascinating area, each chapter starts with introductory material that is motivated by unanswered research questions, includes some history with an occasional anecdote, provides discussions intended to develop intuition, introduces new technical approaches that answer open questions, and raises unsolved research problems. The first chapter, for instance, starts with simple explanations of the apparent "looping" orbit of Mars and the unexpected "Sunrise, Sunset" behavior as viewed from Mercury, to lead up to the unexplained and weird dynamics exhibited by Saturn's F-ring. The second chapter, which introduces a way to decompose the velocity of the system, is motivated by a seemingly easy but unanswered conjecture involving the dynamics of the system when the system's diameter is a constant. The third chapter, which describes questions about the structure of the rings of Saturn, introduces new and surprisingly simple ways to find configurations of the particles that are "central" to any discussion of the N-body problem, or even about those expanding cracks in a car's windshield. The fourth chapter analyzes collisions, while the last chapter discusses the likelihood of collisions and other events."--Jacket.
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Relativistic Many-Body Theory treats — for the first time — the combination of relativistic atomic many-body theory with quantum-electrodynamics (QED) in a unified manner. This book can be regarded as a continuation of the book by Lindgren and Morrison, Atomic Many-Body Theory (Springer 1986), which deals with the non-relativistic theory of many-electron systems, describing several means of treating the electron correlation to essentially all orders of perturbation theory. The treatment of the present book is based upon quantum-field theory, and demonstrates that when the procedure is carried to all orders of perturbation theory, two-particle systems are fully compatible with the relativistically covariant Bethe-Salpeter equation. This procedure can be applied to arbitrary open-shell systems, in analogy with the standard many-body theory, and it is also applicable to systems with more than two particles. Presently existing theoretical procedures for treating atomic systems are, in several cases, insufficient to explain the accurate experimental data recently obtained, particularly for highly charged ions. This shortcoming is expected to be due to omission of combined QED-correlational effects, included in the new unified procedure. All methods treated in Relativistic Many-Body Theory are illustrated with numerical examples. The main text is divided into three parts. In Part I, the standard time-independent and time-dependent perturbation procedures are reviewed. Part II describes three methods for QED calculations, a) the standard S-matrix formulation, b) the Two-times Green’s-function method, developed by the St Petersburg Atomic Theory group, and c) the Covariant-evolution-operator (CEO) method, recently developed by the Gothenburg Atomic Theory group. In Part III, the CEO method is combined with electron correlation to arbitrary order to a unified MBPT-QED procedure. In this procedure the electron correlation can be included to high order, and therefore this procedure is expected to lead to faster convergence than treating the BS equation order by order. Ingvar Lindgren is also the author of the highly-cited "Atomic Many-Body Theory" book published by Springer.
Few-body problem. --- Many-body problem -- Congresses. --- Many-body problem. --- Three-body problem. --- Many-body problem --- Physics --- Physical Sciences & Mathematics --- Atomic Physics --- n-body problem --- Problem of many bodies --- Problem of n-bodies --- Physics. --- Quantum physics. --- Quantum optics. --- Quantum Physics. --- Quantum Optics. --- Optics --- Photons --- Quantum theory --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Mechanics --- Thermodynamics --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Mechanics, Analytic --- Quantum theory.
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Two-body problem --- Many-body problem --- Celestial mechanics --- Congresses --- 521.1 --- -Many-body problem --- -Two-body problem --- -Problem of two bodies --- Mechanics, Analytic --- n-body problem --- Problem of many bodies --- Problem of n-bodies --- Gravitational astronomy --- Mechanics, Celestial --- Astrophysics --- Mechanics --- Celestial mechanics. General principles of dynamical astronomy --- Congresses. --- -Celestial mechanics. General principles of dynamical astronomy --- 521.1 Celestial mechanics. General principles of dynamical astronomy --- -521.1 Celestial mechanics. General principles of dynamical astronomy --- Problem of two bodies --- Two-body problem - Congresses --- Many-body problem - Congresses --- Celestial mechanics - Congresses
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Dynamics --- Numerical analysis --- Mathematical statistics --- Many-body problem --- Astrodynamics --- Congresses --- 531.392 <063> --- 521.1 --- -Dynamics --- -Many-body problem --- -Mathematical statistics --- -Numerical analysis --- -#KVIV --- Mathematical analysis --- Mathematics --- Statistical inference --- Statistics, Mathematical --- Statistics --- Probabilities --- Sampling (Statistics) --- n-body problem --- Problem of many bodies --- Problem of n-bodies --- Mechanics, Analytic --- Dynamical systems --- Kinetics --- Force and energy --- Mechanics --- Physics --- Statics --- Astrophysics --- Astronautics --- Space flight --- Integrals common to various problems of dynamics--Congressen --- Celestial mechanics. General principles of dynamical astronomy --- Statistical methods --- Congresses. --- 521.1 Celestial mechanics. General principles of dynamical astronomy --- 531.392 <063> Integrals common to various problems of dynamics--Congressen --- #KVIV --- Dynamics - Congresses --- Numerical analysis - Congresses --- Mathematical statistics - Congresses --- Many-body problem - Congresses --- Astrodynamics - Congresses --- ASTRODYNAMICS --- DYNAMICS --- MANY BODY PROBLEM --- MATHEMATICAL STATISTICS --- NUMERICAL ANALYSIS --- CONGRESSES
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