瞬时相互作用近似下介子结构波函数的一些探讨(Ⅰ)——瞬时相互作用下介子波函数的一般性质

本文从一对正反费米子结合成束缚态的Bethe-Salpeter方程(以下简称B-S方程)出发,假定正反层子间相互作用可以近似地用质心系瞬时相互作用描写,得到的主要结论如下:(1)B-S方程的求解可归结为在质心系三维空间内进行。描写赝标介子和矢量介子的波函数独立旋量分量的个数分别由4个和8个减少为2个和4个;(2)如果相互作用是空间球对称的,其旋量结构是对角耦合,从赝标介子方程中可以直接看到,束缚态质量作为本征值在方程中是以平方形式出现,同时又可避免四维方程中负激发的困难;(3)在瞬时相互作用近似下给出的结构波函数,可以用来研究束缚态的质量谱和只涉及质心系的过程。

SOME DISCUSSIONS ON THE STRUCTURE WAVE FUNCTIONS OF MESONS FOR THE INSTANTANEOUS INTERACTION APPROXIMATION (Ⅰ)——GENERAL PROPERTIES OF WAVE FUNCTIONS OF MESONS IN THE INSTANTANEOUS INTERACTION CASE

The present paper starts from the Bethe-Salpeter equation for the bound states of a fermion and anti-fermion pair. Assuming that the interaction between the straton and anti-straton can be represented approximately by an instantaneous interaction in the center of mass system, we obtain the following main conclusions: (1) the solution of the Bethe-Salpeter equation may be carried out in ordinary three dimensional space and the numbers of components of the wave functions for the pseudo-scalar and vector mesons reduce respectively from 4 and 8 to 2 and 4; (2) If the interaction is spherically symmetrical in space and its spinor structure is of the diagonal coupling type, then it is seen from the equation for the pseudo-scalar mesons that the meson mass appears as a quadratic eigen value in the equation, without leading to the negative energy excitation usually encountered in the fourdimensional equation; (3) The structure wave function obtained in the instantaneous interaction may be used to study both the mass spectra of the bound states, and the processes involving only the center of mass system.