[FieldX] Inserting ansatz with vector bundle

[Dong-han Yeom (염동한)]

Dear all,

I would like to compute Einstein-Yang-Mills system with a metric and field ansatz. The attached one is my trial. Using the first and second paragraphs, I could derive the equations of motion as a function of F (2-form) or A (1-form).

Now I want to introduce ansatz of metric and A field. I think I can substitute the metric ansatz, but I couldn't insert the A-field part. One of the reason is that the A field has two indices, where one is the spacetime index and the other is the vector bundle index. Eventually, my "ComponentValue" command for A field does not change anything of the real equation.

Could you help me to introduce A field ansatz? Thanks in advance!

Best regards,

Dong-han

[Markus B. Fröb]

Dear Dong-han,

I'm not very familiar with xCoba, so I'm not sure if what I'm writing
below is correct.
Maybe some expert on xCoba can correct me if I'm wrong.
In any case, the full xCoba documentation is here:
http://xact.es/documentation.html

What I understand happens in your notebook is the following: you use a
CTensor for the metric (with SetCMetric[GG, -cb];), but the xCoba
framework to set values for A.
I don't know how well one can mix the two, in any case I prefer CTensor
since it's much more intuitive.

To obtain a CTensor from your rules for A, I used AACTensor =
ToValues@ToCTensor[AA, {-cb, cart}];
Then Eq2[[1]] /. {AA -> AACTensor} gives me output with A substituted.
Of course you still have to define rules for the f tensor, and the
covariant derivative (i.e., the generalised Christoffel symbols).

Best, Markus

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