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Published online by Cambridge University Press: 04 August 2010
This book is devoted to exact solutions of quantum field theory models (in one space dimension plus one time dimension). We also study two-dimensional models of two-dimensional models of classical statistical physics, which are naturally related to these problems. Complete descriptions of the solvable model are given by the Bethe Ansatz which was discovered by H. Bethe in 1931 while studying the Heisenberg antiferromagnet. The Bethe Ansatz has been very useful for the solution of various problems.
Some of the Bethe Ansatz solvable models have direct physical application. A famous problem solved by the Bethe Ansatz is the Kondo problem. Another model is the Hubbard model which is related to high temperature superconductivity. An important application of the Bethe Ansatz is in nonlinear optics where cooperative spontaneous emission of radiation can be described by an exactly solvable quantum model. The Bethe Ansatz is very useful in modern theoretical physics. Correlation functions provide us with dynamical information about the model. They are described in detail in this book.
Bethe Ansatz solvable models are not free; they generalize free models of quantum field theory in the following sense. Many-body dynamics of free models can be reduced to one-body dynamics. With the Bethe Ansatz, many-body dynamics can be reduced to two-body dynamics. The many-particle scattering matrix is equal to the product of two-particle ones.
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