Name: Rolf Mertig (email_not_shown)
Date: 02/21/01-02:15:23 PM Z


Hi,
this seems to be a bug (and it wasn't there some years ago; I cannot
see quickly what causes it).
However, it is easy to work around:

Mathematica 4.1 for Linux
Copyright 1988-2000 Wolfram Research, Inc.
 -- Motif graphics initialized --

In[1]:= !!t.m
<<HighEnergyPhysics`fc`

(* set FI for InputForm and FCE for short external form *)
FI;
amp=SpinorUBar[k].GA[\[Mu]].(1 - \[Lambda] GA[5]).SpinorU[p, m];
Print["amp = ", FCE@amp];

(* using Calc basically expand here the (1-\[Lambda] GA[5]);
   ComplexConjugate works right then
*)
ccamp = ComplexConjugate[ Calc[amp] ];
Print["\n ccamp = ", FCE@ccamp];

(* use FermionSpinSum to do the trace step by step *)
spinsu = FermionSpinSum[ FCI[ Expand[amp ccamp] ] ]
Print["\n spinsu = ", FCE@spinsu];

(* doing the trace *)
r1 = spinsu /. DiracTrace -> Tr;
Print["\n r1 = ", FCE@r1];
 
(* However, one can also do it immediately: *)
 
r2 = SquareAmplitude[ amp ]
Print["\n r2 = ", FCE@r2];
 
(* check it *)
Calc[ r1 - r2]
 
In[1]:= <<t.m
 
FeynCalc4.1.0.3b Type ?FeynCalc for help or visit
http://www.feyncalc.org
$PrePrint is set to FeynCalcForm. Use FI and FC to change the display
format.
amp = SpinorUBar[k] . GA[\[Mu]] . (1 - \[Lambda] GA[5]) . SpinorU[p, m]
         Spinor[Momentum[p], m, 1] . GA[ComplexIndex[\[Mu]]] .
 ccamp =
   Spinor[Momentum[k], 0, 1] + \[Lambda]
   Spinor[Momentum[p], m, 1] . GA[5] . GA[ComplexIndex[\[Mu]]] .
    Spinor[Momentum[k], 0, 1]
          DiracTrace[(m + GS[p]) . GA[ComplexIndex[\[Mu]]] . GS[k] .
 spinsu =
    GA[\[Mu]] . (1 - \[Lambda] GA[5])] +
  \[Lambda] DiracTrace[GS[k] . GA[\[Mu]] . (1 - \[Lambda] GA[5]) .
     (m + GS[p]) . GA[5] . GA[ComplexIndex[\[Mu]]]]
      4 \[Lambda] (\[Lambda] FV[k, ComplexIndex[\[Mu]]] FV[p, \[Mu]] +
 r1 =
     \[Lambda] FV[k, \[Mu]] FV[p, ComplexIndex[\[Mu]]] -
     \[Lambda] MT[\[Mu], ComplexIndex[\[Mu]]] SP[k, p] -
     I LC[\[Mu], ComplexIndex[\[Mu]]][k, p]) +
  4 (FV[k, ComplexIndex[\[Mu]]] FV[p, \[Mu]] +
     FV[k, \[Mu]] FV[p, ComplexIndex[\[Mu]]] -
     MT[\[Mu], ComplexIndex[\[Mu]]] SP[k, p] -
     I \[Lambda] LC[\[Mu], ComplexIndex[\[Mu]]][k, p])
      4 FV[k, ComplexIndex[\[Mu]]] FV[p, \[Mu]] +
 r2 =
             2
  4 \[Lambda] FV[k, ComplexIndex[\[Mu]]] FV[p, \[Mu]] +
  4 FV[k, \[Mu]] FV[p, ComplexIndex[\[Mu]]] +
             2
  4 \[Lambda] FV[k, \[Mu]] FV[p, ComplexIndex[\[Mu]]] -
  4 MT[\[Mu], ComplexIndex[\[Mu]]] SP[k, p] -
             2
  4 \[Lambda] MT[\[Mu], ComplexIndex[\[Mu]]] SP[k, p] -
  8 I \[Lambda] LC[\[Mu], ComplexIndex[\[Mu]]][k, p]
 
Out[1]= 0
---------

Rolf

Timur Rashba wrote:
>
> Hello Rolf!
>
> Sorry for troubling you.
>
> Could you help me in my work with FeynCalc.
> It's very nice package but I couldn't understand some results.
>
> Why
>
> ComplexConjugate[SpinorUBar[k].GA[\[Mu]].(1 - \[Lambda] GA[5]).SpinorU[p, m]]
>
> gave me
>
> Spinor[Momentum[p], m, 1].(1 - \[Lambda] DiracGamma[5]).DiracGamma[
> LorentzIndex[ComplexIndex[\[Mu]]]].Spinor[Momentum[k], 0, 1]
>
> with sign "-" instead of "+" before \[Lambda] DiracGamma[5] ?
>
> It seems to me that it follows from the following:
> in the notation SpinorUBar[k]=SpinorU[k].DiracGamma[0]
> (or DiracGamma[4]) last DiracGamma[0] doesn't take into account in
> ComplexConjugate operation.
>
> Because of this problem I need to write a squared matrix element by hand
> and only after that I can use the command Calc[..] (or
> DiracSimplify[]) to find the results in terms of products of 4-momenta.
>
> Thank you in advance.
>
> Best regards,
> Timur



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