Quantization of non-linear systems

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Abstract
The developments that have taken place over the last five years in semi-classical quantization methods are reviewed. They generalize the WKB method to many degrees of freedom. These techniques, most of which make extensive use of Feynman path integrals, can be extended naturally to quantum field theory, where they have found their most spectacular applications. The basic mathematics are explained by treating, in the path integral formalism, the simple case of the quantization rule of bound states for the one-dimensional Schrodinger equation. The extension to many degrees of freedom is discussed, in particular, how much quantum-mechanical information can be retrieved from given amounts of classical information. The functional integration method is applied to the quantization of classical static or time-dependent solutions of interacting field theories, with particular emphasis on particle-like and bound-state solutions.

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