鉴于反常玻色系统在相对论协变的零质量矢量场中的重要地位和作用,利用Dirac函数的围道积分 形式及其性质,并借助反常玻色系统粒子数表象的完备性特点,重点推导出了反常玻色产生算符的本 征右矢具体的广义解形式,并在此基础上,寻找到与之对应的两组由非共轭反常玻色量子态矢构成的 正交完备性关系,进一步发现此正交完备性关系并不与反常玻色系统中常出现的度规算符相关。作为 上述结论的应用,推导出了量子力学和量子光学中经常出现的两个多项式(Hermite多项式和Laguerre多项式)的 围道积分下的表示式,该表示形式具有普适性,可能对于解决有关以上两个多项式的量子光学问题提供帮助。

Based on the important position and application of abnormal Boson quantum system in the theory of relativistic covariant vector field of zero quality, the specific form of eigenket of the abnormal Boson creation operator can be derived by virtue of the contour integral representation of Dirac-function and its properties as well as feature of the number representation of abnormal Boson system. Furthermore, two sets of new orthogonality and completeness relations, which are irrelevant to normality operator, were obtained. Finally, as an applications, it was used to rewrite the expressions of Hermite polynomial and Laguerre polynomial under meaning of the contour integral, which presumably provide help for some questions of quantum optics about these polynomials.