- #1
bananabandana
- 113
- 5
Given a two particle scattering problem with (initial) relative velocity $|\vec{v}|$, apparently the product $E_{1}$E_{2}|\mathb{v}|$ can be expressed in the covariant form:
$$ E_{1}E_{2}|\vec{v}| = \sqrt{ (p_{1}\cdot p_{2} - m_{1}^{2}m_{2}^{2}} $$
My textbook gives no further explanation - how has this been arrived at?
I tried expanding out:
$$ E_{1}^{2}E_{2}^{2}= (m_{1}^{2}- |\vec{p_{1}}|^{2})(m_{2}^{2}-|\vec{p_{2}}|^{2})$$
But this doesn't seem to go anywhere useful at all.
$$ E_{1}E_{2}|\vec{v}| = \sqrt{ (p_{1}\cdot p_{2} - m_{1}^{2}m_{2}^{2}} $$
My textbook gives no further explanation - how has this been arrived at?
I tried expanding out:
$$ E_{1}^{2}E_{2}^{2}= (m_{1}^{2}- |\vec{p_{1}}|^{2})(m_{2}^{2}-|\vec{p_{2}}|^{2})$$
But this doesn't seem to go anywhere useful at all.