李模型中极点的运动

本文指出,在李模型中,不论有否左方割线和非弹性割线,只要不引入CDD极点,第二叶不具有代表共振态的极点。当CDD极点被引入后,第二叶极点可能在偶合常数增加时穿过正常割线而走入第一叶,但在这以前,另有一极点自左方(或穿过左方割线,或在-∞)走入第一叶。文中画出了一种情形下的二叶的全部极点的运动。

MOTION OF POLES IN THE LEE MODEL

This short paper studies the motion of the poles in the first and the second sheets of the scattering amplitude in the Lee model as the coupling constant g² changes. It is proved that, with or without the left hand cut, with or without the inelastic cut, the theory does not permit the occurrence of poles in the second sheet representing resonances unless the CDD poles are introduced for the inverse amplitude.When the left hand cut is present and the CDD poles are introduced, a pole representing resonance may slip across the normal cut (near the right threshold) into the first sheet as the coupling constant g² increases. But before this occurs, another pole slips into the first sheet across the left hand cut (near the left threshold). Motion of poles in the two sheets is plotted for one such special case.When the left hand cut is absent and the CDD poles are not yet introduced, it is pointed out that no passage of poles of one sheet into another sheet is possible so long as g²>0. When the CDD poles are introduced, such passage becomes possible. It is shown that if a pole in the second sheet slips across the normal cut on increasing g² beyond a certain value g₁²>0, then before g² reaches this value, another pole enters the first sheet at-∞. Needless to say, poles entering from the left usually provide ghosts.These general features are believed to hold for field-theoretical models in general.