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One-dimensional quantum systems show fascinating properties beyond the scope of the mean-field approximation. However, the complicated mathematics involved is a high barrier to non-specialists. Written for graduate students and researchers new to the field, this book is a self-contained account of how to derive the exotic quasi-particle picture from the exact solution of models with inverse-square interparticle interactions. The book provides readers with an intuitive understanding of exact dynamical properties in terms of exotic quasi-particles which are neither bosons nor fermions. Powerful concepts, such as the Yangian symmetry in the Sutherland model and its lattice versions, are explained. A self-contained account of non-symmetric and symmetric Jack polynomials is also given. Derivations of dynamics are made easier, and are more concise than in the original papers, so readers can learn the physics of one-dimensional quantum systems through the simplest model.

Electronic structure --- Matrix inversion. --- Many-body problem. --- n-body problem --- Problem of many bodies --- Problem of n-bodies --- Mechanics, Analytic --- Inverse matrices --- Inverse of a matrix --- Inversion, Matrix --- Linear operators --- Matrices --- Structure, Electronic --- Atomic structure --- Energy-band theory of solids --- Mathematical models. --- Generalized inverses