Name: V. Shtabovenko Date: 02/18/19-06:22:24 AM Z

Ok, after going through the commit log, I see that for Dirac matrices I
introduced the indices via the FermionicChain head

?FermionicChain

FermionicChain[x,i,j] denotes a chain of Dirac matrices x, where the
Dirac indices i and j are explicit. For example,
FermionicChain[DiracGamma[LorentzIndex[mu]],DiracIndex[i],DiracIndex[j]]
denotes a standalone Dirac matrix g^mu_ij. A FermionicChain with only
two arguments denotes a spinor component, e.g.
FermionicChain[Spinor[Momentum[p],m],DiracIndex[i]] stands for the i-th
component of Spinor[Momentum[p],m]

?FermionicChainSimplify

FermionicChainSimplify[expr] simplifies chains of Dirac matrices with
explicit Dirac indices wrapped with a head FermionicChain.

Example

FCI[FermionicChain[SpinorVBar[p1, m1], DiracIndex[i]] FermionicChain[
    GA[mu], DiracIndex[i], DiracIndex[j]]
   FermionicChain[SpinorU[p2, m2], DiracIndex[j]]]
FermionicChainSimplify[%]

However, apart from some basic tests with QGRAF I didn’t pursue it too
much so far.

Cheers,
Vladyslav

Am 18.02.19 um 11:20 schrieb V. Shtabovenko:
> Am 15.02.19 um 16:17 schrieb Mao Zeng:
>> Does FeynCalc have capabilities to contract gamma matrices with
>> explicit spinor indices? For example, if I have an expression like
>> GA[mu][i, j] GA[nu][k, l] GA[rho][j, k], can I use FeynCalc to
>> transform the expression into GA[mu] . GA[rho] . GA[nu]? The
>> nontrivial part is correct ordering of the gamma matrix chain, by
>> following the contraction of the indices (i, j, k, l) above.
>> Similarly, I’m wondering if FeynCalc can perform contraction of SU(N)
>> color matrices with explicit indices, something like SUNT[a][i, j].
>>
>
> For SU(N) matrices this is available since FeynCalc 9.2, cf. Sec 3.7 of
> 1601.01167
>
> For the Dirac matrices I remember pushing some initial code into the dev
> version some time ago, but that was not production ready and not
> sufficiently tested.
>
>> It shouldn’t be hard for me to program this myself, but before I
>> start, I’d like to know if FeynCalc has any built-in functions to
>> handle such index contractions, similar to what can be done by e.g.
>> FormTracer (arXiv:1610.09331).
>
> Well, if it is not hard for you, then do it, after all FeynCalc is all
> about being extendalbe.  BTW, FormTracer can be conveniently employed to
> process FeynCalc expressions and convert the results back into the
> FeynCalc notation. I remember Anton Cyrol (one of the developers)
> showing me several scripts for doing that were only few lines of extra
> code where needed. You can ask him for details.
>
> Cheers,
> Vladyslav
>
>>
>> Thanks for the help!
>>
>