这是一份bath巴斯大学PH20014/PH20061作业代写的成功案

which is simply the Klein-Gordon equation
$$
\left[\eta^{a b} p_{a} p_{b}+m_{e f f}^{2}\right] \psi=0
$$
with a mass term
$$
m_{e f f}^{2}=\frac{2 \mathcal{E}}{D+1} m^{2}
$$
Non-stationary states are superpositions of Klein-Gordon states with different values of $m_{e f f}^{2}$. It can be shown that as long as we only superimpose states with $\varepsilon>0$, i.e. $m_{e f f}^{2}>0$ non-tachyonic, the wavepacket follows a timelike trajectory.
Next, consider minisuperspace models of the form

PPH20014/PH20061 COURSE NOTES ：

$$
\phi=\frac{q}{|\mathbf{r}-\mathbf{b}|}+\delta \phi
$$
wherc
$$
\delta \phi=-q \frac{a}{b} \frac{(\epsilon-1)}{\epsilon+1} I
$$
with
$$
I=\frac{1}{\left(1+y^{2}-2 y \cos \theta\right)^{1 / 2}}-\frac{1}{\gamma y^{1 / \gamma}} \int_{0}^{\gamma} d y^{\prime} \frac{\left(y^{\prime}\right)^{1 / \gamma-1}}{\left(1+y^{\prime 2}-2 y^{\prime} \cos \theta\right)^{1 / 2}}
$$