Tensor density output

[TLa]

Hello everyone,

After defining a tensor of non-zero weight I get the following output (here for weight 1):

I am able to do all kinds of tensor manipulations with this. However, is there a way to fix

the output? 

Best,

Armin

[Jose]

Hi Armin,

xAct has a more powerful way of dealing with weights than just integers. In xAct a density weight is a linear combination of bases objects. As such, this is a concept that can only be properly handled once we have loaded xCoba, because otherwise we cannot define bases. However, there are a few things (mainly PD, weights and determinants) that are defined in advance in xTensor with respect to a fiducial basis/chart that we call AIndex for historical reasons. Therefore what you need here is to use

   WeightOfTensor -> n AIndex

instead of just

   WeightOfTensor -> n

A general weight is of the form

   WeightOfTensor -> n1 basis1 + n2 basis2 + n3 basis3 + ...

where the ni are integers and the basisi have been defined with DefBasis or DefChart. For example the Jacobian between basis1 and basis2 will have weight basis1 - basis2. The weight of the metric with components expressed in a given basis will have weight + 2 basis. And so on.

There is documentation about this in section 1.5 of xCobaDoc.nb. I recommend to read this section.

It's important to note that covariant derivatives do not see weights by default. A given covariant derivative can only respond to weights in a given basis and this is specified with the option WeightedWithBasis of DefCovD.

Cheers,

Jose.

[TLa]

Hello Jose,

that helps a lot, thank you very much!

Best,

Armin