QED_81
Jun4-10, 04:48 AM
1. The problem statement, all variables and given/known data
Hi,
I am given the following action S:
S=1/2∫〖g^ab ((∇_a Ф ∇_b Ф)+(1/6 R_ab Ф^2) ) √(-g) dx^4 〗
Where R_ab is the Ricci tensor, Ф is a scalar field and g^ab is the metric.
I am asked to find the equation of motion for the field.
2. Relevant equations
I know I have to substitute my Lagrangian: L= 1/2 g^ab ((∇_a Ф ∇_b Ф)+(1/6 R_ab Ф^2) )
into the Euler-Lagrange equations, but I don't know in which EL equation exactly!
3. The attempt at a solution
I mean should I use the EL equation where Ф and ∇_b Ф are my independent components? Or should I use the 2nd order EL equations where g_ab; g_ab,c & g_ab,cd are my independent components (as in the Einstein Hilbert action)?
Thanks :)
1. The problem statement, all variables and given/known data
2. Relevant equations
3. The attempt at a solution
Hi,
I am given the following action S:
S=1/2∫〖g^ab ((∇_a Ф ∇_b Ф)+(1/6 R_ab Ф^2) ) √(-g) dx^4 〗
Where R_ab is the Ricci tensor, Ф is a scalar field and g^ab is the metric.
I am asked to find the equation of motion for the field.
2. Relevant equations
I know I have to substitute my Lagrangian: L= 1/2 g^ab ((∇_a Ф ∇_b Ф)+(1/6 R_ab Ф^2) )
into the Euler-Lagrange equations, but I don't know in which EL equation exactly!
3. The attempt at a solution
I mean should I use the EL equation where Ф and ∇_b Ф are my independent components? Or should I use the 2nd order EL equations where g_ab; g_ab,c & g_ab,cd are my independent components (as in the Einstein Hilbert action)?
Thanks :)
1. The problem statement, all variables and given/known data
2. Relevant equations
3. The attempt at a solution