- #1
JorisL
- 492
- 189
Hi,
I was wondering if there exists some software to find the following contraction in an easy way
$$M_{ad}M^{be}M^{cf} f^d_{bc}f^a_{ef}$$
Here the 4x4 metric M has a block diagonal form
$$
\begin{pmatrix}
e^\phi & 0\\
0 & e^{-\phi/3}N
\end{pmatrix}$$
With ##N## a symmetric 3x3 matrix of determinant 1.
The ##f^a_{bc}## are structure constants of some algebra (I have to evaluate this for 13 distinct algebras).
A lot of them are zero, most of the others are 1.
I keep missing terms (due to antisymmetry ##f^a_{bc} = -f^a_{cb}##) when doing any but the most trivial examples by hand.
Thanks,
Joris
I was wondering if there exists some software to find the following contraction in an easy way
$$M_{ad}M^{be}M^{cf} f^d_{bc}f^a_{ef}$$
Here the 4x4 metric M has a block diagonal form
$$
\begin{pmatrix}
e^\phi & 0\\
0 & e^{-\phi/3}N
\end{pmatrix}$$
With ##N## a symmetric 3x3 matrix of determinant 1.
The ##f^a_{bc}## are structure constants of some algebra (I have to evaluate this for 13 distinct algebras).
A lot of them are zero, most of the others are 1.
I keep missing terms (due to antisymmetry ##f^a_{bc} = -f^a_{cb}##) when doing any but the most trivial examples by hand.
Thanks,
Joris