The Many-body Problems

The new edition of this text differs from the old in a number of ways. Classic discoveries which originally had to be omitted owing to lack of space - such as the seminal paper by Fermi, Pasta and Ulam on lack of ergodicity of the linear chain - can now be incorporated. Many applications which did not even exist in 1966 (some of which were spawned by the first edition of this book) are newly included. Among these, the exact solution of the hubbard model, the notion of spinons, the Haldane gap in magnetic spin-one chains, bosonization and fermionization, and a number of other contemporary concerns. Rather than bringing the topic of mathematical physics in one dimension completely up-to-date (self-evidently an impossible task) the authors have opted to complete the picture which they tentatively drew of this field, some 25 years ago in their first edition. This book is not aimed at all the new developments within this period which range from g-ology to string theory to two-dimensional gravity, etc., but has been designed as a most thorough exposition of a limited number of exactly soluble mathematical models of the many-body problem. As such it should serve as a guide and reference book to the classic early literature, while remaining accessible to graduate students and budding professionals in mathematics and theoretical physics. This volume should also provide a useful bridge to much of the current research literature in the topic.