NONLINEAR QUANTIZATION OF INTEGRABLE CLASSICAL-SYSTEMS

It is demonstrated that the so-called ''unavoidable quantum anomalies' ' can be avoided in the framework of a special nonlinear quantization scheme. In this scheme, the quantized Hamiltonians are represented by nonlinear but homogeneous operators in Hilbert space. The nonlinear te rms are of the same order as quantum anomalies, and their role is to c ancel anomalies. The quantization method proposed is applicable to int egrable classical dynamical systems and the result of quantization is again an integrable (but, generally, nonlinear) ''quantum'' system. A simple example is discussed in detail. Irrespective of the existence o f possible physical applications, the method provides a constructive w ay for extending the notion of quantum integrability to nonlinear spec tral problems and gives a practical tool for building completely integ rable nonlinear spectral equations in Hilbert space. (C) 1997 American Institute of Physics.