Name: Vladyslav Shtabovenko (email_not_shown)
Date: 10/21/17-07:20:05 AM Z


> Dear Prffesior,
> I am a research-fellow at a physics institute of India,
> working on "Finite Temperature Field Theory",and "QGP phenomenology".
> I am trying to use Feyncalc for my calculations but facing some problems.
> Let me explain them.
> At finite temperature the propagators and the vertices
> loses the simple Lorentz invariant structure and acquires an admixture
> of both spatial and temporal components. Therefore, to perform these
> calculations the programe should be able to recognige both the zeroth
> and spatial components of a four-vector and know should be able to do
> calculations with DiracGamma[0] and Diracgamma[i],i=1,2,3 explicitly.
> Can such things be done with feynCalc? Plese let me know.
> Sincerly
>
> Purnendu

More than 16 years after the original question, the answer is yes, with FeynCalc 9.3 (aka the current development version) this will be possible.

For example (TGA[] is gamma^0, CGA[i] is gamma^i)

Tr[CGA[i].CGA[j]] (i.e. the trace of two Dirac matrices with Cartesian indices)

yields

-4 CartesianPair[CartesianIndex[i], CartesianIndex[j]]

where CartesianPair[CartesianIndex[i], CartesianIndex[j]] signifies a Kronecker delta

Then

DiracSimplify[TGA[].TGA[]]

yields 1, since gamma^0 gamma^0 =1, while

DiracSimplify[CGA[i, j, i, j]] (i.e. g^i g^j g^i g^j

gives -3

This still needs some testing, performance improvements and a proper documentation,
but this is a work in progress to be completed soon.

Cheers,
Vladyslav



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