这是一份liverpool利物浦大学MATH345的成功案例

$$
\left|K_{T q}(z)-K_{T}(z)\right| \leq \epsilon K_{T}(z)
$$
provided
$$
q r^{*} \leq 1
$$
motivates the introduction of a model for the transverse-current correlator defined by
$$
\bar{\phi}{T q}(z)=-1 /\left[z+q^{2} K{T}(z)\right] .
$$

MATH345 COURSE NOTES ：

$$
K_{T}^{\infty}(z)=-c_{T}^{2} / z
$$
Substitution in yields a correlator
$$
\vec{\phi}{T{q}}^{\infty}(z)=-z /\left[z^{2}-\omega_{T q}^{2}\right]
$$
It has two simple poles on the real frequency axis at $z=\pm \omega_{T q}$, where
$$
\omega_{T q}=c_{T} \cdot q \cdot
$$
The correlator obeys the equation $0=-\omega_{T_{q}}^{2} \bar{\phi}{T q}^{\infty}(z)+z+z^{2} \bar{\phi}{T_{q}}^{\infty}(z)$. Because this result is equivalent to the harmonic-oscillator equation in the time domain
$$
\partial_{t}^{2} \bar{\phi}{T{q}}^{\infty}(t)+\omega_{T_{q}}^{2} \bar{\phi}{T{q}}^{\infty}(t)=0
$$