Name: Frederik Orellana Date: 03/06/01-01:47:07 PM Z

Dear Asesh.

Please notice that I have forwarded this mail to the forum on
www.feyncalc.org, so others (Rolf) can comment too. Please reply to
feyncalc_at_HIDDEN-E-MAIL.

1) It does indeed seem as if there are some problems with the display
function FeynCalcForm. I always work with the FrontEnd interface, so I
didn’t notice. If you load FeynCalc from the FrontEnd e.g.
Spinor[-Momentum[p5], M5, 1] is displayed as a spinor with a negative
momentum argument. Not as u or v. The u or v display is caused by FeynCalc
automatically setting $PrePrint to FeynCalcForm when loaded from the
command line. You can change this behaviour with the commands FI and FC.

v[-p5] should be v[p5] like before. If you evaluate a Spinor alone (not in
a Dot product), this is still the behaviour:

         In[33]:= Spinor[-Momentum[p5], M5, 1]

         Out[33]= v[p5, M5]

The mass argument is not displayed in v[-p5] in the last of your examples.

2) This is a behaviour seen only when working on the command line. So
probably also a problem with FeynCalcForm.

3) The simplification applied to the output by default might have changed
but you can still apply things like DiracSimplify, Calc or Mathematica’s
own Simplify

Points 1 and 2 seem to indicate possible bugs. I will look at this. Rolf,
do you have any comments?

Frederik

At 18:33 05-03-2001 +0100, you wrote:

>Dear Frederik,
>
>I sent you two mails earlier. This time I am sending you a typical
>mathematica file to rum under the FeynCalc. Under the main body of the
>file I pointed out the difference between the outputs from the earlier
>(FeynCalc2.2beta.m (1995)) and the latest versions of FeynCalc.
>
>Specifically I like to understand following specific things. Would you
>kindly find your convenience to help me in this regard.
>
>1. The convention for the spinors: If I use simply the input function
> ‘Spinor’ (which is still there in the new version) to specify the
> spinors, then I am bit confused with the convention adopted for the
> sign of the momentum in the argument of the spinor (for u and v
> spinors). This was somewhat clear in the older version where a
> spinor with a Negative Momentum in the argument is understood to be a
> ‘v-spinor’ with a Positive Momentum. In the outputs pasted below the
> attached Mathematica file, this does not hold.
>
> Please note that for Out[3] in that file the first Spinor is u[-p1]
> from the Old Version while it is v[-p1] from the New version while
> I expect it to be v[p1]. On the other hand, in Out[4], for the Spinor
> v[p5,M5], it is what I expect. The notation somehow depends on whether
> we have a mass for the spinor or not. I pointed it out in one of
> my earlier mails. Please comment.
>
>2. Confusion with Complex Conjugation: The older version conjugates the
> given amplitude so that the coefficients of pl and pr are interchanged
> as compared to the original amplitude. This is not so in the New
> version. Please go through the Out[5].
>
>3. Simplification: Whenever there is a big expression (as is quite common
> with such tedious amplitudes) the degree of simplification had not been
> as usually expected. Could you please comment on whether the DEFAULT
> capacity for Simplification is enhanced in the New Version.
>
>
>Please let me know whether the simple-minded approach I took to realise
>the things really expects too much from the package! Also please let me
>know if I have faltered in some basic issues.
>
>
>Waiting eagerly for your comments.
>With best regards,
> Asesh

(p1s=DiracSlash[p1];
p2s=DiracSlash[p2];
p3s=DiracSlash[p3];
p4s=DiracSlash[p4];
p5s=DiracSlash[p5];
pl= DiracGamma[7];
pr= DiracGamma[6];)

(*
pl=DiracMatrix[7];
pr=DiracMatrix[6];)
*)

LorentzIndex[mu];
LorentzIndex[mup];
LorentzIndex[al];
LorentzIndex[alp];
LorentzIndex[be];
LorentzIndex[bep];

dmu:= DiracMatrix[mu];
dmup:= DiracMatrix[mup];
dal:= DiracMatrix[al];
dalp:= DiracMatrix[alp];
dbe:= DiracMatrix[be];
dbep:= DiracMatrix[bep];

(* pl and pr are helicity projection operators defined above *)

GSZ3A:= CA1 (A1 pl+ A2 pr) FMIX1A + CA2 (A3 pl + A4 pr) FMIX2A;
EEZ:= (pl CLE+ pr CRE);

(* Following are the two fermion lines of a typical Feynman diagram *)

line1SZ3:=Spinor[-p1].dal.EEZ.Spinor[p2];
line2SZ3:=Spinor[p4,M4].dbe.(OL pl+OR pr).(p3s+p5s-MGJ).(GSZ3A).\
           Spinor[-p5,M5];

GNUM:= -MetricTensor[al,be];

(* Amplitude and its hermitian conjugate constructed from the fermion lines *)

ampSZ3:= -I Contract[line1SZ3 GNUM line2SZ3];
campSZ3:= ComplexConjugate[ampSZ3];

spinsumSZ3:= FermionSpinSum[ampSZ3 campSZ3];

traceSZ3:= Tr[spinsumSZ3];

(*######################################################################*)

(* Outputs from Old and New Versions Compared *)

(*

In[3]:= line1SZ3

Out[3]= u[-p1] ga[al] ga[7] CLE + ga[6] CRE u[p2] (*** Old ***)

Out[3]= v[-p1] . ga[al] . (ga[7] CLE + ga[6] CRE) . u[p2] (*** New ***)
-————————————————————————-

line[4]:= line2SZ3

Out[4]= u[p4, M4] ga[be] ga[7] OL + ga[6] OR gs[p3] + gs[p5] - MGJ

   (ga[7] A1 + ga[6] A2) CA1 FMIX1A + (ga[7] A3

   v[p5, M5] (*** Old ***)

Out[4]= u[p4, M4] . ga[be] . (ga[7] OL + ga[6] OR) .

   (gs[p3] + gs[p5] - MGJ) . ((ga[7] A1 + ga[6] A2) CA1 FMIX1A +

     (ga[7] A3 + ga[6] A4) CA2 FMIX2A) . v[p5, M5] (*** New ***)

-—————————-

In[5]:= ComplexConjugate[%]

Out[5]= v[p5, M5] (ga[6] A1 + ga[7] A2) CA1 FMIX1A +

    (ga[6] A3 + ga[7] A4) CA2 FMIX2A gs[p3] + gs[p5] - MGJ ga[6] OL + ga[7] OR

   ga[be*] u[p4, M4] (*** Old ***)

Out[5]= v[-p5] . ((ga[7] A1 + ga[6] A2) CA1 FMIX1A +

     (ga[7] A3 + ga[6] A4) CA2 FMIX2A) . (gs[p3]

   (ga[7] OL + ga[6] OR) . ga[be*] . u[p4, M4] (*** New ***)

*)