- #1
Alex Petrosyan
- 33
- 10
I was wondering where does the 1/2 factor come from in the Euler-Lagrange equation, that is:
[tex]
L = \sqrt{g_{\mu \nu} \dot{x}^\mu \dot{x}^\nu}
[/tex]
implies that [tex] \partial_\mu L = \pm \frac{1}{2} (\partial_\mu g_{\mu \nu} \dot{x}^\mu \dot{x}^\nu )[/tex]
I'm not sure I entirely understand where it comes from. Intuitively, it might be because taking the partial derivative also is a contraction, but every book I've looked in, simply assumes this is true, and I don't understand how.
[tex]
L = \sqrt{g_{\mu \nu} \dot{x}^\mu \dot{x}^\nu}
[/tex]
implies that [tex] \partial_\mu L = \pm \frac{1}{2} (\partial_\mu g_{\mu \nu} \dot{x}^\mu \dot{x}^\nu )[/tex]
I'm not sure I entirely understand where it comes from. Intuitively, it might be because taking the partial derivative also is a contraction, but every book I've looked in, simply assumes this is true, and I don't understand how.