FeynCalc manual (development version)

Kinematics

See also

Overview.

Manipulations of scalar products

FeynCalc allows you to specify the values of scalar products before doing the calculation.

SP[p, q] = s;

SP[p, q]

$$s$$

FV[q, \[Mu]] FV[q, \[Nu]] (FV[p, \[Mu]] FV[p, \[Nu]] - MT[\[Mu], \[Nu]]/SP[p, p])
% // Contract

$$\overline{q}^{\mu } \overline{q}^{\nu } \left(\overline{p}^{\mu } \overline{p}^{\nu }-\frac{\bar{g}^{\mu \nu }}{\overline{p}^2}\right)$$

$$s^2-\frac{\overline{q}^2}{\overline{p}^2}$$

To clear the previously set values, use

FCClearScalarProducts[]

SP[p, q]

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

FV[q, \[Mu]] FV[q, \[Nu]] (FV[p, \[Mu]] FV[p, \[Nu]] - MT[\[Mu], \[Nu]]/SP[p, p])
% // Contract

$$\overline{q}^{\mu } \overline{q}^{\nu } \left(\overline{p}^{\mu } \overline{p}^{\nu }-\frac{\bar{g}^{\mu \nu }}{\overline{p}^2}\right)$$

$$(\overline{p}\cdot \overline{q})^2-\frac{\overline{q}^2}{\overline{p}^2}$$

A good habit is to always apply FCClearScalarProducts[] before setting the values, like in

FCClearScalarProducts[];
SP[p1, p1] = m1^2;
SP[p2, p2] = m2^2;

Setting up the kinematics in advance improves performance of FeynCalc and leads to more compact results. The results with the fully arbitrary kinematics are the most complicated and the longest ones.