标题： 玻色子$sp(4,R)$表示的变形及其子代数 显示英文标题

标题： Deformations of the Boson $sp(4,R)$ Representation and its Subalgebras

摘要： 该sp(4,R)代数的玻色子表示及其两种不同的变形被考虑，以及每个代数的紧致和非紧致子代数。初始表示以及变形表示都在相同的福克空间中作用。其中一种变形表示基于玻色子产生和湮灭算符的标准q变形。sp(4,R)的子代数（紧致u(2）和三个非紧致u(1,1）的表示）也被变形，并包含在这个变形代数中。它们在sp(4,R）的作用空间中是可约的，并分解为不可约表示。另一种变形表示通过将q变形的玻色子转换为关于标准变形su(2）的q张量（类似旋量）来实现。其所有生成元都被变形，并且可以用类似旋量算符的张量积表示。在这种情况下，另一种su(2）的变形自然地作为子代数出现，并可以解释为角动量代数so(3）的变形。其表示是可约的，并分解为不可约表示，从而提供了相同的完整描述。 显示英文摘要

摘要： The boson representation of the sp(4,R) algebra and two distinct deformations of it, are considered, as well as the compact and noncompact subalgebras of each. The initial as well as the deformed representations act in the same Fock space. One of the deformed representation is based on the standard q-deformation of the boson creation and annihilation operators. The subalgebras of sp(4,R) (compact u(2) and three representations of the noncompact u(1,1) are also deformed and are contained in this deformed algebra. They are reducible in the action spaces of sp(4,R) and decompose into irreducible representations. The other deformed representation, is realized by means of a transformation of the q-deformed bosons into q-tensors (spinor-like) with respect to the standard deformed su(2). All of its generators are deformed and have expressions in terms of tensor products of spinor-like operators. In this case, an other deformation of su(2) appears in a natural way as a subalgebra and can be interpreted as a deformation of the angular momentum algebra so(3). Its representation is reducible and decomposes into irreducible ones that yields a complete description of the same.