Name: Vladyslav Shtabovenko
Date: 08/13/15-10:12:12 PM Z
This is another example that calls for TensorFunction
LC2sh[x_, y_] := TensorFunction[{LC2, “A”}, x, y]
res = (Tr[
GS[p].GA[\[Mu]].(x2*GS[p] +
GS[q]).GA[\[Beta]].(x*GS[p] +
GS[q]).GA[\[Alpha]].(x1*GS[p]
- GS[q]).GA[\[Nu]]]*
LC2sh[\[Alpha], \[Beta]]/8) // Contract
// Collect2[#, LC2] &
-> 2 (x x1 FV[p, \[Mu]] FV[p, \[Nu]]
- x x2 FV[p, \[Mu]] FV[p, \[Nu]] -
x FV[p, \[Nu]] FV[q, \[Mu]] + x1
FV[p, \[Nu]] FV[q, \[Mu]] +
x FV[p, \[Mu]] FV[q, \[Nu]] - x2
FV[p, \[Mu]] FV[q, \[Nu]]) LC2[
Momentum[p], Momentum[q]] -
LC2[LorentzIndex[\[Nu]],
Momentum[q]] (x x1 FV[p, \[Mu]]
SP[p, p] -
x x2 FV[p, \[Mu]] SP[p, p] - 2 x FV[q,
\[Mu]] SP[p, p] +
x1 FV[q, \[Mu]] SP[p, p] + x2 FV[q,
\[Mu]] SP[p, p] +
2 x FV[p, \[Mu]] SP[p, q] - 2 x2 FV[p,
\[Mu]] SP[p, q]) -
LC2[LorentzIndex[\[Mu]],
Momentum[q]] (x x1 FV[p, \[Nu]]
SP[p, p] -
x x2 FV[p, \[Nu]] SP[p, p] + 2 x FV[q,
\[Nu]] SP[p, p] -
x1 FV[q, \[Nu]] SP[p, p] - x2 FV[q,
\[Nu]] SP[p, p] -
2 x FV[p, \[Nu]] SP[p, q] + 2 x1 FV[p,
\[Nu]] SP[p, q]) -
LC2[LorentzIndex[\[Nu]],
Momentum[p]] (x x1 x2 FV[p, \[Mu]]
SP[p, p] +
x1 x2 FV[q, \[Mu]] SP[p, p] + 2 x x2
FV[p, \[Mu]] SP[p, q] +
2 x FV[q, \[Mu]] SP[p, q] - x FV[p,
\[Mu]] SP[q, q] +
2 x2 FV[p, \[Mu]] SP[q, q] + FV[q,
\[Mu]] SP[q, q]) +
LC2[LorentzIndex[\[Mu]],
Momentum[p]] (x x1 x2 FV[p, \[Nu]]
SP[p, p] +
x1 x2 FV[q, \[Nu]] SP[p, p] + 2 x x1
FV[p, \[Nu]] SP[p, q] +
2 x FV[q, \[Nu]] SP[p, q] - x FV[p,
\[Nu]] SP[q, q] +
2 x1 FV[p, \[Nu]] SP[q, q] + FV[q,
\[Nu]] SP[q, q]) -
LC2[LorentzIndex[\[Mu]],
LorentzIndex[\[Nu]]] (x x1 x2 SP[p, p]^2
- x x1 SP[p, p] SP[p, q] +
x x2 SP[p, p] SP[p, q] + x1 x2 SP[p, p]
SP[p, q] +
2 x SP[p, q]^2 - x SP[p, p] SP[q, q] + x1
SP[p, p] SP[q, q] +
x2 SP[p, p] SP[q, q] + SP[p, q] SP[q,
q])
>
>
> Okay so now I’m having the opposite problem, its not throwing out
symmetric terms. For example:
>
> In: FV[p, LorentzIndex[a]] FV[p,
LorentzIndex[b]] Eps[a, b]
>
> Out: p^a p^b \[Epsilon]^(a b)
>
> In: Contract[%]
>
> Out: p^a p^b \[Epsilon]^(a b)
>
> In: Simplify[%]
>
> Out: p^a p^b \[Epsilon]^(a b)
>
> In: Calc[%]
>
> Out: p^a p^b \[Epsilon]^(a b)
>
> And in my actual calculation:
>
> In:
tr1=Calc[Contract[Tr[GS[p].GA[\[Mu]].(x2*GS[p]+GS[q]).GA[\[Beta]].(x*GS[p]+GS[q]).GA[\[Alpha]].(x1*GS[p]+GS[q]).GA[\[Nu]]]*LC[\[Alpha],\[Beta]]]/8]
>
> Out: -((LeviCivita(\[Alpha], \[Beta], Dimension
-> 4) g^(\[Alpha] \[Nu])
> g^(\[Beta] \[Mu]) Q^4)/(4 xb)) + …
-((LeviCivita(\[Alpha], \[Beta], Dimension -> 4)
g^(\[Alpha] \[Beta])
> g^(\[Mu] \[Nu]) Q^4)/(4 xb)) + …
>
> Where the second term is zero and …’s represent the numerous terms
I left out
>
> I feel I’m missing some basic thing here that’s holding me back
seeing as I’ve had this work properly in the past in different
situations.