Quadratic covariant derivatives nabla A (Weyl)

[Manuele Cossari]

Hi everyone,

in my lagrangian I have terms   as cd[-a][cd[-b][A[b]]]  or cd[-b][cd[b][A[-a]]] of Weyl vector,

I would like to split  it in symmetric and antisymmetric parts.

How can do it?

Thank you for your help,

Manuele

[TB]

Hi!

Does this conversation answer your question?

https://groups.google.com/g/xact/c/O6oTsKzfd8c/m/oZjINA3oAgAJ

Regards
Thomas

[Manuele Cossari]

A bit,

for example; I can write a term cd[-a][cd[b][A[a]]] in this way:

DefTensor[F[-a,-b],M, Antysimmetric]     

F[b,a]  =PD[b][A[a]] - PD[a][A[b]]

rule=MakeRule[{cd[-a][cd[b][A[a]]] , 1/2cd[-a] (cd[b][A[a]] + cd[a][A[b]]) + 1/2cd[-a][F[b,a]]}]

and maybe introducing 

DefTensor[S[-a,-b],M, Simmetric]      

S[a,b] :=cd[b][A[a]] + cd[a][A[b]]

rule1=MakeRule[{cd[-a][cd[b][A[a]]] , 1/2cd[-a] [S[a,b]] + 1/2cd[-a][F[b,a]]}]

?

Thank you foryour help :)

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