 Lorentz boost

A Lorentz boost relates inertial frames moving at a constant relative velocity without an additional spatial rotation. In units with light speed one, the displayed transformation preserves $t^2-x^2$, with Lorentz factor $\gamma =(1-v^2{)}^{-1/2}$. Applying it to a static classical field-theory soliton produces a uniformly moving solution in a Lorentz-invariant theory.

Two observers travel at fixed speed relative to each other. They synchronize origins at x=0 and t=0, and their spacial axes are perfectly aligned. This is a subset of the Lorentz group. TODO confirm it does not form a subgroup however.