- #1
Dixanadu
- 254
- 2
Hey everyone,
So I've come across something in my notes where it says that these two Lagrangian densities are equal:
[itex]\mathcal{L}_{1}=(\partial_{mu}\phi)^{\dagger}(\partial^{\mu}\phi)-m^{2}\phi^{\dagger}\phi[/itex]
[itex]\mathcal{L}_{2}=-\phi^{\dagger}\Box\phi - m^{2}\phi^{\dagger}\phi[/itex]
where [itex]\Box = \partial^{\mu} \partial_{\mu}=\frac{1}{c^{2}}\frac{\partial^{2}}{\partial t^{2}}-\nabla^{2}[/itex]
How does this come about? I know that the second term in each density is equal of course, but the first term in each...how are they equal? can someone explain please?
Thank you!
So I've come across something in my notes where it says that these two Lagrangian densities are equal:
[itex]\mathcal{L}_{1}=(\partial_{mu}\phi)^{\dagger}(\partial^{\mu}\phi)-m^{2}\phi^{\dagger}\phi[/itex]
[itex]\mathcal{L}_{2}=-\phi^{\dagger}\Box\phi - m^{2}\phi^{\dagger}\phi[/itex]
where [itex]\Box = \partial^{\mu} \partial_{\mu}=\frac{1}{c^{2}}\frac{\partial^{2}}{\partial t^{2}}-\nabla^{2}[/itex]
How does this come about? I know that the second term in each density is equal of course, but the first term in each...how are they equal? can someone explain please?
Thank you!