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## Homework Statement

I have two four vectors v and w with [tex] v^{2} = m^{2} > 0, v_{0} > 0 [/tex] and [tex] w^{2} > m^{2}, w_{0} > 0 [/tex]. Now we consider a system with

[tex] w' = (w_{0}', \vec{0}) [/tex] and [tex] v' = (v_{0}', \vec{v} \, ') [/tex] and in addition we consider the quantity [tex] \lambda = \vert \vec{v}' \vert \, \sqrt{ w_{0}'^{2} - m^{2}} [/tex]. Now I should find a Lorentz invariant expression of [tex] \lambda [/tex] only using the invariants [tex]v^{2}, w^{2}, vw[/tex].

## Homework Equations

## The Attempt at a Solution

I think I've found a solution: [tex] t = \sqrt{\dfrac{(vw)^{2} - v^{2} w^{2}}{v^{2}} (v^{2} - w^{2})} [/tex].

But I'm not really sure if this "solution" is really Lorentz invariant (my problem is the square root). Could anyone confirm this solution or is there any mistake?