协变谐振子的重子结构模型及其K—S变换求解

假定重子中轻层子间不存在三体力，并把满足约束P_i²+U(x²)+m_i²=0（ｉ＝１，２）的二质点组的相对论力学应用于重子的ＳＵ₃模型，取Ｕ（ｘ²）形为α＋ｂｘ²，通过适当坐标平移，可以将重子中的内部运动等效为两个协变谐振子。采用Ｋｕｓｔａｎｈｅｉｍｏ－Ｓｔｉｅｌ变换（简称Ｋ—Ｓ变换），可将它们化为两个三维氢原子问题。这样，在求解中能关键词：

KUSTANNHEIMO -STIEFEI TRANSFORMATION OF BARY-ON STRUCTURE MODEL WITH A FOUR-DIMENSI-ONAL COVARIANT HARMONIC OSCILLATOR

In this paper, we assume there exist no three-body forces in a baryon. So that the constraint equations for two particles P_i²+U(x²)+m_i²=0 (i=1，2 )can be applied to the SU₃ model of the baryon. Next, we take U(x²) as a+bx². By use of a proper coordinate transformation, the internal motion of the baryon can be reduced to double covariant harmonic oscillators. From the Kustannheimo-Stiefel transformation, the problem of a covariant harmonic oscillator can be transformed to that of a threedimensional hydrogen atom with constranits. On that basis, the difficulty of the excitation of the time degree of freedom can be avoided naturally and the mass-squared formula for baryons can be obtained.