# Lorentz invariance

1. Feb 24, 2009

### parton

1. The problem statement, all variables and given/known data

I have two four vectors v and w with $$v^{2} = m^{2} > 0, v_{0} > 0$$ and $$w^{2} > m^{2}, w_{0} > 0$$. Now we consider a system with
$$w' = (w_{0}', \vec{0})$$ and $$v' = (v_{0}', \vec{v} \, ')$$ and in addition we consider the quantity $$\lambda = \vert \vec{v}' \vert \, \sqrt{ w_{0}'^{2} - m^{2}}$$. Now I should find a Lorentz invariant expression of $$\lambda$$ only using the invariants $$v^{2}, w^{2}, vw$$.

2. Relevant equations

3. The attempt at a solution

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

2. Feb 24, 2009

### Avodyne

The square root is OK as long as what you're taking the root of is positive. I didn't check your math, but the answer should look something like this.