Year: 1997
Type: article
Abstract: 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 terms are of the same order as quantum anomalies, and their role is to cancel anomalies. The quantization method proposed is applicable to integrable 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 of possible physical applications, the method provides a constructive way for extending the notion of quantum integrability to nonlinear spectral problems and gives a practical tool for building completely integrable nonlinear spectral equations in Hilbert space.
Source: Journal of Mathematical Physics
DOI: 10.1063/1.532084
Authors: Antonio Scotti, Alexander Ushveridze
Institutions: University of Parma, University of Łódź
Language: English
Topic: Nonlinear Waves and Solitons
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2122044648