Relativistic Invariance Part Two

[Ed Quanta]

I am asked to prove that the d'Alembertian operator (the 4 dimensional Laplacian operator) |_|^2 is a lorentz invariant operator. Do I just multiply the Lorentz transformation matrix by the second partial derivatives with respect to four space?

[turin]

Originally posted by Ed Quanta
I am asked to prove that the d'Alembertian operator (the 4 dimensional Laplacian operator) |_|^2 is a lorentz invariant operator. Do I just multiply the Lorentz transformation matrix by the second partial derivatives with respect to four space? I suppose you could do that. But I would just show that it is a scalar. Show that it is a contraction of a 1st rank tensor with itself. Use the Minkowski metric tensor to raise the index of one of the partial derivatives and it should be obvious.