**Next message:**V. Shtabovenko: "Problem using OneLoop"**Previous message:**Vladyslav Shtabovenko: "Re: A question"**Maybe in reply to:**Thibaut Cousin: "Feyncalc refuses to expand LC"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Mail actions:**[ respond to this message ] [ mail a new topic ]

Although FeynCalc 9.3 still cannot go into single components of Lorentz

tensors, it can distinguish between temporal and spatial components, so

that one can do the following:

ex = LC[a, b, c, d] FourVector[k1, a] FourVector[k2, b] FourVector[k3,

c] FourVector[k4, d] // LorentzToCartesian // Contract

which yields

TC[k4] CLC[][k1, k2, k3] - TC[k3] CLC[][k1, k2, k4] +

TC[k2] CLC[][k1, k3, k4] - TC[k1] CLC[][k2, k3, k4]

Here TC[x] stands for x^0, i.e.

?TC

TC[p] is the temporal component of a 4-vector and is transformed into

TemporalPair[TemporalMomentum[p], TemporalIndex[]] by FeynCalcInternal,

while CLC is the Cartesian 3D epsilon tensor

?CLC

CLC[m,n,r] evaluates to Eps[CartesianIndex[m], CartesianIndex[n], \

CartesianIndex[r]] applying FeynCalcInternal. CLC[m,...][p, ...] \

evaluates to Eps[CartesianIndex[m], ..., CartesianMomentum[p], ...] \

applying FeynCalcInternal.

That is, CLC[][a,b,c] is precisely the triple product a. (b x c)

So, given the explicit values of the components of k1, k2, k3 and k4

we can write something like

explicit[k1] = Table[k1[i], {i, 1, 3}];

explicit[k2] = Table[k2[i], {i, 1, 3}];

explicit[k3] = Table[k3[i], {i, 1, 3}];

explicit[k4] = Table[k4[i], {i, 1, 3}];

ex /. FCI[CLC[][a_, b_, c_]] :> Dot[explicit[a], Cross[explicit[b],

explicit[c]]] /. {FCI@TC[x_] :> x[0]}

which gives

(k1[3] (-k2[2] k3[1] + k2[1] k3[2]) +

k1[2] (k2[3] k3[1] - k2[1] k3[3]) +

k1[1] (-k2[3] k3[2] + k2[2] k3[3])) k4[0] -

k3[0] (k1[3] (-k2[2] k4[1] + k2[1] k4[2]) +

k1[2] (k2[3] k4[1] - k2[1] k4[3]) +

k1[1] (-k2[3] k4[2] + k2[2] k4[3])) +

k2[0] (k1[3] (-k3[2] k4[1] + k3[1] k4[2]) +

k1[2] (k3[3] k4[1] - k3[1] k4[3]) +

k1[1] (-k3[3] k4[2] + k3[2] k4[3])) -

k1[0] (k2[3] (-k3[2] k4[1] + k3[1] k4[2]) +

k2[2] (k3[3] k4[1] - k3[1] k4[3]) +

k2[1] (-k3[3] k4[2] + k3[2] k4[3]))

Cheers,

Vladyslav

*> -----BEGIN PGP SIGNED MESSAGE-----
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*> Hash: SHA1
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*>
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*> Hello,
*

*>
*

*> I'm using version 4.1.1 on Mathematica 4.0.
*

*> The problem arises when I have the following expression:
*

*>
*

*> x=LC[a,b,c,d]FourVector[k1,a]FourVector[k2,b]FourVector[k3,c]FourVector[k4,d]
*

*>
*

*> I have previously given the value of all possible scalar products. I want
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*> Feyncalc to expand x using these scalar products.
*

*> I've tried to use every possible Feyncalc command, without success. On the
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*> other hand, if I ask it to compute Calc[x*x], it works! I've checked by hand,
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*> the result is correct, but then I loose the sign of x.
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*> Is there a way to make Feyncalc expand a single LC contraction? Is it a bug?
*

*> Regards,
*

*>
*

*> - --
*

*> Thibaut Cousin
*

*> email : cousin@in2p3.fr
*

*> web : http://clrwww.in2p3.fr
*

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*> iD8DBQE9Edubv1vqsTa1E4oRAmirAJ0U9rs4s3GZp0fKqaAifH63+MiJlwCeKFLt
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*> bCHzefaloBVUOCXE+WjFOWc=
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*> =3Q63
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