Euler Lagrange equation and a varying Lagrangian

  • #1

Homework Statement:

The variation of the Lagrangian with respect to PSI and X

Relevant Equations:

Euler Lagrange equation
Hello, I have been working on the three-dimensional topological massive gravity (I'm new to this field) and I already faced the first problem concerning the mathematics, after deriving the lagrangian from the action I had a problem in variating it
Here is the Lagrangian
Sans titre.png


The first variation should be with respect to Ψ I tried to find this result
22.png

but I had a sign different, my result had a Minus sign.

The second variation is with respect to the vector X, note that
55.png

and the result is
1593770698677.png

I tried to use the euler lagrange equation to find this result but i don't have much experience dealing with this wedge product variation

thank you in advanced
 

Answers and Replies

Related Threads on Euler Lagrange equation and a varying Lagrangian

Replies
8
Views
3K
Replies
5
Views
1K
Replies
2
Views
1K
  • Last Post
Replies
14
Views
5K
Replies
3
Views
1K
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
6
Views
3K
Replies
5
Views
2K
Replies
2
Views
1K
  • Last Post
Replies
3
Views
2K
Top