- #1
binbagsss
- 1,259
- 11
Homework Statement
Using the E-L equations to get the EoM from the action.
Homework Equations
I am using E-L equations in the form:
## \frac{\partial}{\partial_u} \frac{\partial L}{\partial_u \phi}-\frac{\partial L}{\partial \phi} ##
where ##L ## is the Lagrangian
The Attempt at a Solution
I am a bit confused with the term ## \frac{1}{2} \partial_u \phi \partial^u \phi ## of a lot of actions.
The correct answer is ## \frac{1}{2} \partial_u \partial^u \phi ##
As it is for the first term of the EoM from [1] I get:
## \frac{\partial}{\partial_u} \frac{1}{2} \partial^u \phi = \frac{1}{2}\partial_u \partial^u \phi ##
However if I write it as ##\frac{1}{2}(\partial_u \phi)^2 ## , the factor of half cancels, but my indices don't work out :
## \frac{\partial}{\partial_u} \partial_u \phi = \partial_u \partial_u \phi ##Many thanks