x

## 留言板

 引用本文:
 Citation:

## SOME REMARKS ON THE THEORY OF EXPANSORS

CHANG TSUNG-SUI
PDF
• #### 摘要

本文讨论展开子的一些性质。将展开子Anrst变换至ξ表示,定义为〈ξ|〉=∑ξ0-n-1ξ1rξ2sξ3tAnrst,立即可以看出〈ξ|〉在洛伦兹变换中的变换,正如标准表示中的变换。由此可以立即证明,在标志洛伦兹群的各种不可约表示的两个量J=-1/2IklIkl,I=1/2εklmnIklImn中,对於展开子而言,I一定等於零。我们也证明了如果我们要求J的本徵函数〈ξ|〉在各处行为正常,便获得J1/2;(ii)I′=±(1+J)1/2i,J′=1+J。我们又证明了ξvξv?/(?ξμ)/(ξμ)-(1±(1+J)1/2)ξμ将(J,0)空间变为(1+J±2(1+J)1/2,0)空间。利用上式中取“-”符号的算符,我们可以构成一个像(-irμpμ+k)ψ=0的波动方程,其中ψ只在两个展开子空间中。

#### Abstract

This paper is a brief discussion of the properties of expansors introduced by Dirac(1945). After transforming the expansors Anrst to ξ-representation defined by 〈ξ|〉=∑ξ0-n-1ξ1rξ2sξ3tAnrst (1) and showing that undergoes transformations identical with standardrepresentations in a Lorentz transformation, it is shown that of the two fundamental invariants J=-1/2IklIkl,I=-1/2εklmnIklImn (2) characterizing the different irreducible representations of the Lorentz group, the second one in the theory of expansors is always zero. It is also shown that the requirement of the different eigenfunctions of J in the space to behave regularly for all ratios of ξ leads to J1/2, (3) (ii)I′=±(1+J)1/2i,J′=1+J.(4) Explicit formula for such matrixes are also worked out.If we require expansors after operations by such operators remain as expansors, we must let -1≤J≤0 and confine ourselves to the selection rule I′=0,J′=1+J-2(1+J)1/2. (5) Since successive transformations of J by the above formula starting with an initial value of J, say J1, satisfying -1≤J1≤0 do not lead to values of J beyond J1 and J2 J2≡1+J1-2(1+J1)1/2 (both J1, J2 being negative), it is clear that in constructing a wave equation of the type (-irμpμ+k)ψ=0 (6) with ψ in expansor spaces, the simplest formulation is to let the space of ψ to consist of two such expansor spaces (J1 0), (J2,0). Of course, the matrixes γμ are so choosen that only the selection rule (5) is effective. It is shown that the operators ξvξv?/(?ξμ)-(1±(1+J)1/2)ξμ (7) transform the (J,0) space to the spaces (1+J±2(1+J)1/2,0) respectively. Thus γμ may be constructed easily in terms of the operator ξvξv?/(?ξμ)-(1-(1+J)1/2)ξμ. Investigations of such wave equations will be left later.

#### 参考文献

 [1]

#### 施引文献

•  [1]
•  [1] 曹永军, 云国宏, 那日苏. 平面波展开法计算二维磁振子晶体带结构. 物理学报, 2011, 60(7): 077502. doi: 10.7498/aps.60.077502 [2] 上官丽英, 孙洪祥, 陈秀波, 温巧燕, 朱甫臣. 三粒子纠缠W态隐形传态的正交完备基展开与算符变换. 物理学报, 2009, 58(3): 1371-1376. doi: 10.7498/aps.58.1371 [3] 郑 强, 岳 萍, 龚伦训. Jacobi椭圆函数展开解的可视化. 物理学报, 2005, 54(7): 2996-2999. doi: 10.7498/aps.54.2996 [4] 张满红, 朱邦芬, 黄绮, 王文新, 周均铭. 用推广的平面波展开法检验平面内极化的电子子带跃迁. 物理学报, 1997, 46(2): 393-399. doi: 10.7498/aps.46.393 [5] 何祚庥, 张肇西, 黄涛. 关于复合场场论的微扰展开式. 物理学报, 1976, 25(3): 215-225. doi: 10.7498/aps.25.215 [6] 张宗燧. 微扰展开的解析性. 物理学报, 1961, 17(1): 1-17. doi: 10.7498/aps.17.1 [7] 余友文, 张宗烨. 关於镧La57的超精细结构. 物理学报, 1958, 14(6): 488-496. doi: 10.7498/aps.14.488 [8] 黄祖洽. 关於中子在两种介质中的慢化问题. 物理学报, 1958, 14(2): 153-162. doi: 10.7498/aps.14.153 [9] 向仁生. 关於铬矾单晶的顺磁各向异性. 物理学报, 1957, 13(3): 177-180. doi: 10.7498/aps.13.177 [10] 钱临照；刘民治. 关於锡单晶体的微蠕变. 物理学报, 1956, 12(3): 275-279. doi: 10.7498/aps.12.275 [11] 蒋曼英. 关於电子光学中的Petzval系数. 物理学报, 1956, 12(5): 439-446. doi: 10.7498/aps.12.439 [12] 朱洪元. 关於核子的磁矩. 物理学报, 1956, 12(1): 85-86. doi: 10.7498/aps.12.85 [13] 葛庭燧, 钱知强, 卡列尔·密歇克. 关於镍中含碳所引起的内耗峰. 物理学报, 1955, 11(5): 403-410. doi: 10.7498/aps.11.403 [14] 田渠. 关於中子磁矩的计算. 物理学报, 1955, 11(5): 425-428. doi: 10.7498/aps.11.425 [15] 刘叔仪. 关於固体的现实应力空间(续). 物理学报, 1954, 10(3): 171-186. doi: 10.7498/aps.10.171 [16] 刘叔仪. 关於固体的现實应力空间. 物理学报, 1954, 10(1): 13-34. doi: 10.7498/aps.10.13 [17] . 关於人名英譯的声明. 物理学报, 1953, 9(1): 2-2. doi: 10.7498/aps.9.2 [18] 黄祖洽. 关於氟化氢分子的一个计算. 物理学报, 1951, 8(1): 57-63. doi: 10.7498/aps.8.57 [19] 邓稼先. 关於氢二核之光致蜕变. 物理学报, 1951, 8(2): 170-182. doi: 10.7498/aps.8.170 [20] 束星北. 关於波动方程式之“超前解”. 物理学报, 1950, 7(6): 97-104. doi: 10.7498/aps.7.97
• 文章访问数:  6459
• PDF下载量:  384
• 被引次数: 0
##### 出版历程
• 收稿日期:  1958-05-19
• 刊出日期:  1958-05-20

/