I'm trying to get into quantum field theory, I've seen Einstein notation before and I think I'm grasping it fairly well, but I've ran into two things that I just could not figure out and they both involved derivatives, or gradients.(adsbygoogle = window.adsbygoogle || []).push({});

My problem is just mathematical, doesn't have to do with the physics at all.

Can anyone please help me understand the following from the bookAn introduction to quantum field theory by Peskin and Schroeder. I have another issue, but I don't want this post to get too long and I'm hoping that if I understand this I will understand my other problem as well:

==================================

The book gives the following:

[tex]\mathcal{L}=\frac{1}{2}(\partial_{\mu}\phi)^{2}-\frac{1}{2}m^{2}\phi^{2}[/tex]

Now, the thing I don't understand is that the book says if we use this lagrangian with the Euler-Lagrange equation:

[tex]\partial_{\mu}\left( \frac{\partial\mathcal{L}}{\partial(\partial_{\mu}\phi)}\right)-\frac{\partial\mathcal{L}}{\partial\phi}=0[/tex]

and they say that plugging that lagrangian into the above will give:

[tex](\partial^{\mu}\partial_{\mu}+m^{2})\phi=0[/tex]

Now, when I try to work this out I get this instead:

[tex](\partial_{\mu}\partial_{\mu}+m^{2})\phi=0[/tex]

which is obviously wrong I think, but I don't understand where the raised subscript comes from in their answer.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Einsten notation, 4-gradients

Loading...

Similar Threads for Einsten notation gradients |
---|

I Braket notation question |

I Confused about Dirac Notation |

I Double sided arrow notation in Dirac Field Lagrangian |

B Teacher needs help: Bra–ket notation for parabolas? |

I Does slowing light with a BEC change any of its properties? |

**Physics Forums | Science Articles, Homework Help, Discussion**