- #1
Tamin Ayoub
- 1
- 0
- 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
The first variation should be with respect to Ψ I tried to find this result
but I had a sign different, my result had a Minus sign.
The second variation is with respect to the vector X, note that
and the result is
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
Here is the Lagrangian
The first variation should be with respect to Ψ I tried to find this result
but I had a sign different, my result had a Minus sign.
The second variation is with respect to the vector X, note that
and the result is
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