electromagnetism - Reason why $F^{munu}F_{munu}$ and $tilde{F}_{munu}F^{munu}$ are Lorentz invariant

I'm trying to think of an intuitive reasoning for why $F^{\mu\nu}F_{\mu\nu}$ and $\tilde{F}_{\mu\nu}F^{\mu\nu}$ are Lorentz invariant. By this I mean that I don't simply want to show that they remain unchanged after actually performing a Lorentz transformation and seeing that I end up with the same expressions, but some sort of 'deeper' understand of why this is so. I just can't really think of why these expressions (written out in vectors like $E^2 - B^2$ and $B \cdot E$ with some constants) would be the same for every inertial observer, while for a space-time interval I can sort of grasp this.

Is there perhaps a good reference someone could point me to?

Answer

They're lorentz scalars. Every scalar is lorentz invariant.