中山大学学报自然科学版 ›› 2010, Vol. 49 ›› Issue (3): 152-154.

• 研究论文 • 上一篇    

关联函数解析式的另一种推导方法

方锡岩,冯开喜,丘斯伟,张宏浩   

  1. (中山大学物理科学与工程技术学院,广东 广州 510275)
  • 收稿日期:2009-07-09 修回日期:1900-01-01 出版日期:2010-05-25 发布日期:2010-05-25
  • 通讯作者: 张宏浩

Another Derivation of Analytic Expression of Correlation Function

FANG Xiyan, FENG Kaixi, QIU Siwei, ZHANG Honghao   

  1. (School of Physics and Engineering, Sun Yetsen University, Guangzhou 510275, China)
  • Received:2009-07-09 Revised:1900-01-01 Online:2010-05-25 Published:2010-05-25

摘要: 探讨了d维欧氏空间中自由标量场的关联函数,用两种不同的方法推导求得了它的解析表达式,其中第二种方法为该文提出。文献上一般只讨论了到3维以及更低维空间的结果,作者推广得到了任意维的结果。计算3维空间的关联函数的方法一般是在3维空间的球坐标下直接进行积分求解,该文也应用这种方法在d维空间的球坐标系下直接积分得到了推广的结果。另一方面,发现可以通过选取合适的坐标系可有效地降低积分动量的维数,同样可以求得关联函数的解析式来。两种方法虽然用到的技术不同,但经过复杂的运算之后所得到的结果是一致的,结果表明:任意维空间的自由标量场的关联函数与变形Bessel函数只差一个有理因子,其中变形Bessel函数的阶数是由空间的维数所决定。

关键词: 关联函数, 积分维数约化, 欧氏空间

Abstract: The analytic expression of correlation function of free scalar field in any dimensional Euclidean space is derived by two different methods, the second of which is proposed. The results in 3 and lower dimensional space are generally discussed in the literature, and the generalized result in arbitrary dimensional space is obtained. When studying the case in 3dimensional space, people often do the integration directly in the 3dimensional space using the sphere coordinates, and this method is also applied in this paper to get the generalized result. On the other hand, it is found that choosing the appropriate coordinate system can effectively reduce the integration variable dimension and finally arrive at the same result. The result shows that the correlation function of free scalar field in any dimensional space is related to the modified Bessel function, whose order is determined by the space dimension.

Key words: correlation function, reduction of integration variable dimension, Euclidean space

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