Name: V. Shtabovenko Date: 03/05/20-10:54:52 PM Z

Hi,

this expression vanishes by the virtue of Schouten’s identity.

It has already been mentioned multiple times in this forum, so

<https://www.google.com/search?as_q=site%3Afeyncalc.org+OR+site%3Afeyncalc.github.io+OR+site%3Agithub.com%2FFeynCalc\&q=schouten>

should return enough pointers.

There’s an old function called “Schouten” which can help if the identity
needs to be applied only once or perhaps twice

ex = Plus[
   Times[Eps[LorentzIndex[n], LorentzIndex[o], LorentzIndex[p],
     Momentum[v]], Pair[LorentzIndex[m], Momentum[v]]],
   Times[-1,
    Eps[LorentzIndex[m], LorentzIndex[o], LorentzIndex[p],
     Momentum[v]], Pair[LorentzIndex[n], Momentum[v]]],
   Times[Eps[LorentzIndex[m], LorentzIndex[n], LorentzIndex[p],
     Momentum[v]], Pair[LorentzIndex[o], Momentum[v]]],
   Times[-1,
    Eps[LorentzIndex[m], LorentzIndex[n], LorentzIndex[o],
     Momentum[v]], Pair[LorentzIndex[p], Momentum[v]]],
   Times[Eps[LorentzIndex[m], LorentzIndex[n], LorentzIndex[o],
     LorentzIndex[p]], Pair[Momentum[v], Momentum[v]]]]

ex // Schouten
(*0*)

It is also not always satisfactory that it doesn’t tell you which rule
exactly
was applied to simplify the expression. This is why at some point I added
a more advanced version called FCSchoutenBruteForce.

https://feyncalc.github.io/FeynCalcBook/ref/FCSchoutenBruteForce.html

It doesn’t really do anything clever, yet in many cases I was able to use it
even for quite complicated expressions that required dozens of successive
applications of the identity.

For the case at hand there is not much difference, since the expression is
simple enough. For more involved situations FCSchoutenBruteForce is a better
tool than Schouten alone.

ex // FCSchoutenBruteForce[#, {}, {}] &
(*0*)

Cheers,
Vladyslav

Am 05.03.20 um 20:56 schrieb Martin Jung:
> Hi,
> I have an issue with FeynCalc not being able to simplify an expression:
> the expression reads
> Plus[Times[Eps[LorentzIndex[n],LorentzIndex[o],LorentzIndex[p],Momentum[v]],Pair[LorentzIndex[m],Momentum[v]]],Times[-1,Eps[LorentzIndex[m],LorentzIndex[o],LorentzIndex[p],Momentum[v]],Pair[LorentzIndex[n],Momentum[v]]],Times[Eps[LorentzIndex[m],LorentzIndex[n],LorentzIndex[p],Momentum[v]],Pair[LorentzIndex[o],Momentum[v]]],Times[-1,Eps[LorentzIndex[m],LorentzIndex[n],LorentzIndex[o],Momentum[v]],Pair[LorentzIndex[p],Momentum[v]]],Times[Eps[LorentzIndex[m],LorentzIndex[n],LorentzIndex[o],LorentzIndex[p]],Pair[Momentum[v],Momentum[v]]]]
> and should be zero (since this is the difference of twice evaluating the same expression with FeynCalc in two different ways). However, even when assigning explicit values to the Lorentz indices, I cannot get this expression to vanish explicitly.
> Thanks in advance for your help and sorry, should this be a rookie mistake (I’ve searched for a long time for a solution before posting).
>