Abstract
In this paper, we define what we call a “unitary immersion” of a nonlinear system. We observe that, for classical Hamiltonian systems, this notion contains, in some sense, the concept of “quantization.” We restrict our attention to “degree-zero unitary immersions,” where all “observation functions” must be represented by operators of the type “multiplication by a function.” We show that the problem of classifying such “degree-zero unitary immersions” of a given nonlinear system is not obvious. In some cases, we solve this problem.
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Gauthier, J.P., Guérin, J.P. Unitary immersions of nonlinear systems. Math. Systems Theory 19, 135–153 (1986). https://doi.org/10.1007/BF01704911
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DOI: https://doi.org/10.1007/BF01704911