osp（2，1）超代数及其相关物理系统的实现

正交辛李超代数osp（1）的表示|4）和抛物玻色子相干态

Representations of the orthosymplectic Lie superalgebra osp(1|4) and paraboson coherent states

引入并获得了多模抛物玻色子相干态。在适当的子空间中，这些相干态提供了单位的分解，其中当使用猫型态表示时，测量是正定的。还得到了相互交换的降低算子对角化的双相干态。计算了相干态基中的矩阵元。

李超代数osp（1）的仿射Fock空间和酉不可约表示|2n）

The paraboson Fock space and unitary irreducible representations of the Lie superalgebra osp(1|2n)

已知正交辛李超代数osp（1）的定义关系|2n）等价于n对抛物算子$b^\pm_i$的定义（三元）关系.特别地，在通常的星条件下，这意味着“p阶抛物子"对应于osp（1）的酉不可约（无限维）最低权表示V（p| 2n）。除了简单的情况p=1或n=1，这些表示从来没有被构造由于计算困难，尽管他们的重要性。在本文中，我们给出了这些表示V（p）的一个明确而优美的构造，并给出了osp（1）的明确作用或矩阵元素|2n）发电机。V（p）的正交基向量用Gelfand-Zetlin模式表示，其中osp（1）的子代数u（n|（2）起着关键作用。我们的结果还导出了这些无穷维OSP（1）的特征公式|2n）陈述。进一步考虑分支$ osp(1|2n) \supset sp(2n) \supset u(n)$，我们得到了sp（2n）的显式无穷维酉不可约最低权表示及其特征标.

A class of infinite-dimensional representations of the Lie superalgebra osp(2m+1|2n) and the parastatistics Fock space

An orthogonal basis of weight vectors for a class of infinite-dimensional representations of the orthosymplectic Lie superalgebra osp(2m+1|2n) is introduced. These representations are particular lowest weight representations V(p), with a lowest weight of the form [-p/2,...,-p/2|p/2,...,p/2], p being a positive integer. Explicit expressions for the transformation of the basis under the action of algebra generators are found. Since the relations of algebra generators correspond to the defining relations of m pairs of parafermion operators and n pairs of paraboson operators with relative paraferm…

非相对论自由粒子的超对称性和超相干态

Supersymmetry and Supercoherent States of a Nonrelativistic Free Particle

给出了正交辛超代数osp（2/2）在平方可积函数的Hilbert超空间中的坐标非典型表示。量子非相对论性自由粒子哈密顿量是这个超代数的一个元素，它是这个系统的动力学超代数。利用超群位移算符定义了超相干态，并明确地构造了超相干态。这些是已知的非典型抽象超群$OSp(2/2)$相干态的坐标表示。我们从经典力学的观点把所得结果解释为一种经典粒子的模型，这种粒子在相超空间的偶数扇区中是不动的，而在其奇数扇区中（在适当的坐标系中）作直线运动。

Representations of the Lie superalgebra $B(\infty,\infty)$ and parastatistics Fock spaces

The algebraic structure generated by the creation and annihilation operators of a system of m parafermions and n parabosons, satisfying the mutual parafermion relations, is known to be the Lie superalgebra osp(2m+1|2n). The Fock spaces of such systems are then certain lowest weight representations of osp(2m+1|2n). In the current paper, we investigate what happens when the number of parafermions and parabosons becomes infinite. In order to analyze the algebraic structure, and the Fock spaces, we first need to develop a new matrix form for the Lie superalgebra B(n,n)=osp(2n+1|2n), and construct …

The parastatistics Fock space and explicit Lie superalgebra representations

It is known that the defining triple relations of m pairs of parafermion operators and n pairs of paraboson operators with relative parafermion relations can be considered as defining relations for the Lie superalgebra osp(2m+1|2n) in terms of 2(m+n) generators. With the common Hermiticity conditions, this means that the parastatistics Fock space of order p corresponds to an infinite-dimensional unitary irreducible representation V(p) of osp(2m+1|2n), with lowest weight (-p/2,...,- p/|p/2,...,p/2). These representations (also in the simplest case m=n=1) had never been constructed due to comput…