关于层子模型中的电磁形式因子与结构波函数的积分表示

虽然从B-S方程出发,用谐振子位势来讨论介子的质谱,可以得到较好的结果,但是当用这样得到的近似波函数来计算电磁形式因子时,却给出形式因子对类空的q²为复数。本文指出,出现上述不合理结果的原因,在于所得的近似波函数不具有正确的对P₀的解析性。为了保证这种解析性同时又使波函数保持协变形式,比较适当的方法是,利用戴逊证明的定理将波函数写成积分表示。另外,根据波函数在x=0点为有限的物理要求,我们还给出了积分表示中的谱函数所应满足的一些求和条件。

NOTE ON THE ELECTROMAGNETIC FORM FACTOR AND INTEGRAL REPRESENTATION OF THE WAVE FUNCTION IN THE STRATON MODEL

Although the meson mass spectrum calculated from the simple harmonic potential by the B-S equation fits the experimental data fairly well, the wave function so obtained leads however to unreasonable results when applied to calculate the electromagnetic form factor, which turns out to be complex for space-like q². It is argued that the reason for this lies in the fact that such a wave function does not possess the correct analytical property for the variable p₀. In order to guarantee this analyti-city as well as to maintain the covariant form, it is adequate to express the wave function in the form of an integral representation according to a theorem proved by Dyson. Furthermore, some summation rules for the spectral function in the integral representation are derived with the physical condition that the wave function should be finite at x = 0.