Problem in AllContractions

[Ali rezaie]

Hi

I know that  AllContractions[] can be used for All possible contractions.when I used it for some derivatives and some fields the program does not work as the arXiv:1308.3493v1 by Teake Nutma.

I wanted to see all possible independent term with [\phi\phi\phi\PD\PD\PD\PD] but it gave me nothing except errors .my \phi has got 2 indexes.

Could someone please help me how I can find all possible independent terms with this structure?

I would like to see all possible terms. then I would like to omit some of the terms for example /. \phi^a_a=0 is it true after AllContractions[]?

How can I do?

Many thanks in advance.

Ali

[Mario Herrero Valea]

Hi, 

It works for me with this simple code. Just take into account that derivatives must be acting on something, thus the definition of the dummy tensor.

<< xAct`xTras`

DefManifold[M, dim, IndexRange[{a, z}]];

DefMetric[1, gm[-a, -b], CD, {";", "\[PartialD]"}, WeightedWithBasis -> AIndex];

DefTensor[phi[a, b], M]

DefTensor[dummy[], M]

AllContractions[phi[a, b] phi[c, d] CD[e]@CD[f]@CD[g]@CD[h]@dummy[]]

Later on you can set phi[a,-a] to zero with a rule.

Cheers,

Mario

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[Ali rezaie]

Dear Mario

many thanks for replying.

I could not operate your code as well.I am writing like Team Nutma but I have a problem yet for simpler cases which is not my case.

The problem which is in arXiv:1308.3493v1 :

DefManifold[M, dim, IndexRange[a,m]];

DefMetric[-1, metric[-a,-b], PD, PrintAs -> "η",FlatMetric -> True, SymbolOfCovD -> {",","∂"}];

SetOptions[SymmetryOf, ConstantMetric -> True]; 

DefTensor[H[-a, -b], M, Symmetric[{-a, -b}], PrintAs -> "h"];

DefTensor[xi[a], M, PrintAs -> "ξ"];

Sterms = AllContractions[ H[a, b] PD[c]@PD[d]@H[e, f] ]

IT is the error:

ParallelCombine::nopar: No parallel kernels available; proceeding with sequential evaluation. >>

I will attach the pic of my text as well. I hope to solve this with your help.

Best

[Ali rezaie]

It works, but I would like to see all possible independent terms with 3 fields and 4 derivatives.

Is there any way to help me more or not?

many thanks.

Ali