Solution
= Solution
The <Lorentz transformation> is $t'=\gamma(t-vx)$, $x'=\gamma(x-vt)$ in units $c=1$. Adding and subtracting gives
$$
p'=\gamma(1+v)(t-x),\qquad q'=\gamma(1-v)(t+x).
$$
Since $\gamma(1+v)=\sqrt{(1+v)/(1-v)}$ and the other factor is its reciprocal,
$$
\boxed{p'=\alpha p,\qquad q'=q/\alpha,\qquad\alpha=\sqrt{\frac{1+v}{1-v}}=e^\eta.}
$$
Here $\eta$ is the boost <rapidity>. Their product is unchanged, as required by invariance of the <Minkowski interval>.