as the product RB,
where R is a rotation and B a boost. The generic boost matrix is
(Jackson, eq. (11.98)):
We want to write a generic Lorentz matrix as the product RB,
where R is a rotation and B a boost. The generic boost matrix is
(Jackson, eq. (11.98)):
where 
are the Cartesian components of the boost velocity 
.
On the other hand, R is of the form
where 
is a three-dimensional rotation matrix. The problem is to
determine B and R, given 
We can keep the indices consistently placed (up or down) by rewriting B in the form
where 
are covariant components. We find
hence 
and
or explicitly
