FeynCalc Memo

This is a memo for FeynCalc.

Install

I found a good blog (in Japanese) explaining how to install FeynCalc.
FeynCalc｜ひかるのブログ
Let me copy it. (I try to translate it in English)

1. Download HighEnergyPhysics-xxx.tar.gz, and untar.
2. Show Mathematica icon in Finder or folder, and right click it.
3. Choose "Show Package Contents".
4. Move files you get in 1. to Addons/Applications/
5. Boot Mathematica. If you have already booted it, quit it and
reboot.

(Actually, I downloaded fc803.tar.gz. But how to install is same.)

When we use FeynCalc, do

<< HighEnergyPhysics`FeynCalc`

New installation Method

After version 9, installation became easy. See official site. Put a few command on Mathematica.
We can start FeynCalc by

<< FeynCalc`

Some Commands

# gamma5, PL, PR

DiracGamma[5] is \[Gamma]^5.
DiracGamma[6] is (1+\[Gamma]^5)/2. 
DiracGamma[7] is (1-\[Gamma]^5)/2.

# momentum, scalar product

p^{mu} = FV[p,mu] = Pair[Lorentz[mu], Momentum[p] ].
p^{mu} k_{mu} = ScalarProduct[p,k] = Pair[Momentum[p], Momentum[k] ].

# Four-vector in D-dimension is FVD[p,mu]

# Trace is Tr, but it does not work with FVD[___]. Use FV[___].

# four-divergence

FourDivergence[ FeynmanDenominator[p,m], FV[p,a]] = 0
FourDivergence[ 1/(ScalarProduct[p,p] - m^2), FV[p,a]] \neq 0

# contraction (\gamma^\mu \gamma_\mu in D-dimension)

MTD[mu, nu]
GAD[mu].GAD[nu]
%% * % //DiracSimplify

Momentum derivative


FourDivergence[FV[p,a], FV[p,b]]

= g^{a,b}
or
FourDivergence[ (FV[p,a])/(ScalarProduct[l-p,l-p]), FV[p,b]]

If you want p^a -> 0 after calculation, do %/.{Pair[_,Momentum[p]]->0}

help file

When you need to know what kind of commands are prepared, you can see the help file. However, you may wonder how to use the help file. Actually, I spent 30 minutes to find how to use it... I hope the following steps will help you to use the help file.

(1) click "documentation center" shown after loading FeynCalc.
two-external-gluons

(2) Help file is shown, but not helpful yet. Move the pointer to the right.
two-external-gluons

(3) "]]" appear. Click one of them.
two-external-gluons

(4) Now help file helps you.
two-external-gluons