Symmetry of The Levi-Civita Tensor with Partial Derivatives

[Alejandro Guarnizo Trilleras]

Dear all,

I'm computing now a Scalar-vector Lagrangian with self-interactions. The idea es simply to build blocks of derivatives of a vector field, and a scalar field, which afterwards should be contracted with metric tensors, or the Levi-Civita tensor (to avoid neglect possible contributions). When doing that, and simplifying the evaluation, I found terms that are contractions of the Levi-Civita tensor and second partial derivatives of the scalar field. This term should be zero, since is basically the contraction of a symmetric tensor with and anti-symmetric one. However, I could not handle with this. I appreciate any suggestions.

Thanks!

[ghadir jafari]

Dear Alejandro  

Setting:

$CommuteCovDsOnScalars = True;

at the beginning of your file solve this problem. But After all I suggest using AllContraction commands, assuming  F and *F as independent and find all possible contractions.

See the file. 

[Alejandro Guarnizo Trilleras]

Dear Ghadir,

Have a nice day. It seems to work!..thanks a lot. However I found that only works for second order derivatives. It seems commutation for third order derivatives of a scalar field does not work :(