- #1

McLaren Rulez

- 292

- 3

Hi,

Can anyone show me how to prove that the differential operator, i.e [itex]\partial_{\mu}[/itex] is Lorentz covariant. In other words, [itex]\partial /\partial x'_{\nu}=\Lambda^{\nu}_{\mu}\partial /\partial x^{\mu}[/itex].

And once this is done, how can I show that the D'Alembert operator [itex]\partial_{\mu}\partial^{\mu}[/itex] is a four vector in the sense that its magnitude is a constant in all frames? I understand that all four vectors have a constant magnitude so but I am not sure how to apply this when dealing with differential operators.

Thank you

Can anyone show me how to prove that the differential operator, i.e [itex]\partial_{\mu}[/itex] is Lorentz covariant. In other words, [itex]\partial /\partial x'_{\nu}=\Lambda^{\nu}_{\mu}\partial /\partial x^{\mu}[/itex].

And once this is done, how can I show that the D'Alembert operator [itex]\partial_{\mu}\partial^{\mu}[/itex] is a four vector in the sense that its magnitude is a constant in all frames? I understand that all four vectors have a constant magnitude so but I am not sure how to apply this when dealing with differential operators.

Thank you

Last edited: