The d'Alembertian operator, denoted as |_|^2, is confirmed to be a Lorentz invariant operator. To demonstrate this, one should show that it is a scalar quantity, achieved by proving it as a contraction of a first-rank tensor with itself. Utilizing the Minkowski metric tensor to raise the index of one of the partial derivatives simplifies the proof. This approach is more effective than merely multiplying the Lorentz transformation matrix by the second partial derivatives.
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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.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?