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This self-contained monograph addresses the flow equation approach to many-particle systems. The flow equation approach consists of a sequence of infinitesimal unitary transformations and is conceptually similar to renormalization and scaling methods. Flow equations provide a framework for analyzing Hamiltonian systems where these conventional many-body techniques fail. The text first discusses the general ideas and concepts of the flow equation method. In a second part these concepts are illustrated with various applications in condensed matter theory including strong-coupling problems and non-equilibrium systems. The monograph is accessible to readers familiar with graduate- level solid-state theory.

Many-body problem. --- Unitary transformations. --- Hamiltonian systems. --- Particles (Nuclear physics) --- Quantum field theory. --- Condensed matter. --- Problème des N corps --- Systèmes hamiltoniens --- Particules (Physique nucléaire) --- Théorie quantique des champs --- Matière condensée --- Particles (Nuclear physics). --- Physics --- Physical Sciences & Mathematics --- Atomic Physics --- Condensed materials --- Condensed media --- Condensed phase --- Materials, Condensed --- Media, Condensed --- Phase, Condensed --- Relativistic quantum field theory --- Elementary particles (Physics) --- High energy physics --- Nuclear particles --- Nucleons --- Hamiltonian dynamical systems --- Systems, Hamiltonian --- Transformations, Unitary --- n-body problem --- Problem of many bodies --- Problem of n-bodies --- Physics. --- Condensed Matter Physics. --- Theoretical, Mathematical and Computational Physics. --- Liquids --- Matter --- Solids --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Field theory (Physics) --- Quantum theory --- Relativity (Physics) --- Nuclear physics --- Differentiable dynamical systems --- Mechanics, Analytic --- Transformations (Mathematics) --- Mathematical physics. --- Physical mathematics --- Mathematics