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On the nonlinearity interpretation of q- and f-deformation and some applications

V. I. Man'ko·R. Vilela Mendes
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Abstract

q-oscillators are associated to the simplest non-commutative example of Hopf algebra and may be considered to be the basic building blocks for the symmetry algebras of completely integrable theories. They may also be interpreted as a special type of spectral nonlinearity, which may be generalized to a wider class of f-oscillator algebras. In the framework of this nonlinear interpretation, we discuss the structure of the stochastic process associated to q-deformation, the role of the q-oscillator as a spectrum-generating algebra for fast growing point spectrum, the deformation of fermion operators in solid-state models and the charge-dependent mass of excitations in f-deformed relativistic quantum fields.

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V. I. Man'ko, R. Vilela Mendes. 1997-05-22. On the nonlinearity interpretation of q- and f-deformation and some applications. https://doi.org/10.1088/0305-4470/31/28/017

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