Is 2EN^2 dx^3 a Relativistic Invariant?

[Magister]

Homework Statement

Prove that the quantity $2EN^2 dx^3$ is a relativistic invariant.

Homework Equations

Well we want to prove that this quantity is the same in all inercial frames.
My doubt is with the energy transformation,

$$E=\gamma E_0$$

does it transforms like that? If yes,$$dx^3=\frac{dx_0^3}{\gamma}$$

$$2EN^2 dx^3=2 \gamma E_0 N^2 \frac{dx^3}{\gamma}=2E_0 N^2 dx_0^3$$

and its done...?

Thanks

 

[dextercioby]

Do you know the covariant formalism ? If you do, you might know that $$p_{\mu}x^{\mu}$$ is a Lorentz scalar. Assume a Lorentz boost in the positive Ox direction...Can you continue from here ?

P.S. What does N stand for ?

 

[Magister]

I have done it. That result is correct. Thanks a lot.
By the way N stands for a normalization factor that cames, I guess, from the wave function.