**Next message:**V. Shtabovenko: "Re: chargeconjugationmatrix"**Previous message:**Purnendu Chakraborty: "(no subject)"**In reply to:**Purnendu Chakraborty: "(no subject)"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Mail actions:**[ respond to this message ] [ mail a new topic ]

You can define custom tensors, cf. for example

https://mathematica.stackexchange.com/questions/148680/defining-a-two-index-field-in-feyncalc

but those normally do not care about any special properties. Although

you can of course add those properties (e.g. symmetries or special

behavior when contracted with particular vectors) "by hand". The

decompositions would need some user defined functions, though.

There is for example a toy addon FVProjection that implements the

decomposition of a 4-vector into transverse and longitudinal components

along the direction of the given vector

$LoadAddOns = {"FVProjection"};

<< FeynCalc`

FVProjectionL[x, mu, p, Dimension -> D]

FVProjectionT[x, mu, p, Dimension -> D]

Another useful example is the function LorentzToCartesian in the

development version

that decomposes Lorentz tensors into their temporal and spatial components:

https://github.com/FeynCalc/feyncalc/blob/master/FeynCalc/Lorentz/LorentzToCartesian.m

I believe that with some will and motivation you can write the stuff you

need along these lines.

Cheers,

Vladyslav

Am 22.10.18 um 17:02 schrieb Purnendu Chakraborty:

*> I missed this response to my old question. I am looking forward to see this implementation. Thank you for your great works.
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*>
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*> I have also some suggestion. Is it possible for an user to define new objects and corresponding algebra without touching internal structures of FeynCalc? For example, metric tensor in (t,z) or (x, y)
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*> space :
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*> g_\par^{\mu\nu} = diag(1, 0, 0, -1), g_\perp^{\mu\nu} = diag(0, -1, -1, 0)
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*> such that
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*> g^{\mu\nu} = g_\par^{\mu\nu} + g_\perp^{\mu\nu}
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*>
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*> Four vectors and Gamma matrices are decomposed accordingly. These structures appear in QFT calculation in presence of a background magnetic field.
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*>
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*>
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*>
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