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.
>
> 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)
> space :
> g_\par^{\mu\nu} = diag(1, 0, 0, -1), g_\perp^{\mu\nu} = diag(0, -1, -1, 0)
> such that
> g^{\mu\nu} = g_\par^{\mu\nu} + g_\perp^{\mu\nu}
>
> 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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