查看“快度”的源代码

== Rapidity ==

First,we know:
\[
arctanh(x)=\frac{1}{2}\ln\frac{1+x}{1-x}
\]

Then define:

'''rapidity'''
\[
  w=arctanh{\frac{v}{c}}=arctanh{\frac{|p|c}{E}}=\frac{1}{2}\ln\frac{E+|p|c}{E-|p|c}
\]

'''pseudorapidity'''
\[
\eta=arctanh{\frac{v_z}{v}}=arctanh{\frac{|p_z|}{|p|}}=\frac{1}{2}\ln\frac{|p|+|p_z|}{|p|-|p_z|}=-\ln(\tan(\frac{\theta}{2}))
\]

'''rapidity in high energy experiment'''
\[
y=arctanh{\frac{v_z}{c}}=arctanh{\frac{|p_z|c}{E}}=\frac{1}{2}\ln\frac{E+|p_z|c}{E-|p_z|c}
\]