Non-abelian gauge fields with xTensor?

[Giulia Pagano]

Hi all,

I would like to define a non-abelian gauge field and the related field strength (the group is SU(N)). Is there a built-in way to do that in xTensor? In particular, I would like to know if there is a way to handle gauge indices and structure constants.

Thank you,

Giulia

[Leo Stein]

Hi Giulia,

Yes and no. You can create a vector bundle with DefVBundle, and a connection which is aware of that bundle with DefCovD. See Sec. 6.10 of xTensorDoc.nb for an example. This will define two sets of connection coefficients and curvatures — those for the horizontal (tangent) indices, and those for the vertical (bundle) indices.

However, there is not yet the concept of a structure group or any other structures for a bundle. If you want a metric on that bundle, you will have to define one yourself, and if you want structure constants, you will similarly have to define those yourself.

Best

Leo

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[Giulia Pagano]

Thank you Leo, I will try that way.

Regards,

Giulia

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