FeynCalc manual (development version)

PairContract2

PairContract2 is like Pair, but with local contraction properties. It works best with products of Pairs that are expected to evaluate to a product of scalar products.

• Suitable contractions between products of PairContract2 symbols are evaluated immediately.
• Momenta are never expanded and every PairContract2 symbol containing Momentum in both slots is immediately converted to a Pair.
• BMHV algebra is not supported, every tensor must be purely 4 or D-dimensional

PairContract2 is an auxiliary function used in higher level FeynCalc functions that require fast contractions between multiple expressions, where Contract would be too slow.

See also

Overview, Contract, PairContract, PairContract3.

Examples

Pair[LorentzIndex[\[Mu]], Momentum[p]] Pair[LorentzIndex[\[Mu]], Momentum[q]] 
 
% /. Pair -> PairContract2

$$\overline{p}^{\mu } \overline{q}^{\mu }$$

$$\overline{p}\cdot \overline{q}$$

Pair[LorentzIndex[\[Mu]], Momentum[p + q]] Pair[LorentzIndex[\[Mu]], Momentum[r + s]] 
 
% /. Pair -> PairContract2

$$\left(\overline{p}+\overline{q}\right)^{\mu } \left(\overline{r}+\overline{s}\right)^{\mu }$$

$$(\overline{p}+\overline{q})\cdot (\overline{r}+\overline{s})$$