标题： 关于q-和f-变形的非线性解释及其一些应用 显示英文标题

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

摘要： q-振子与最简单的非交换HOPF代数例子相关，可以被视为完全可积理论对称代数的基本构建块。 它们也可以被解释为一种特殊的谱非线性类型，这种非线性可以推广到更广泛的f-振子代数类中。 在这一非线性解释的框架下，我们讨论与q-变形相关的随机过程的结构，q-振子作为快速增长点谱的谱生成代数的作用，固体模型中费米子算符的变形，以及f-变形相对论量子场中激发态的电荷依赖质量。 显示英文摘要

摘要： 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.