CartesianScalarProduct[p, q] is the input for the scalar product of two Cartesian vectors p and q.
CartesianScalarProduct[p] is equivalent to CartesianScalarProduct[p, p].
Expansion of sums of momenta in CartesianScalarProduct is done with ExpandScalarProduct.
Scalar products may be set, e.g. via CartesianScalarProduct[a, b] = m^2; but a and b may not contain sums.
CartesianScalarProduct[a] corresponds to CartesianScalarProduct[a,a]
Note that ScalarProduct[a, b] = m^2 actually sets Cartesian scalar products in different dimensions specified by the value of the SetDimensions option.
It is highly recommended to set CartesianScalarProducts before any calculation. This improves the performance of FeynCalc.
CartesianScalarProduct[p, q]\overline{p}\cdot \overline{q}
CartesianScalarProduct[p + q, -q]-\left(\overline{q}\cdot (\overline{p}+\overline{q})\right)
CartesianScalarProduct[p, p]\overline{p}^2
CartesianScalarProduct[q]\overline{q}^2
CartesianScalarProduct[p, q] // StandardForm
(*CartesianPair[CartesianMomentum[p], CartesianMomentum[q]]*)CartesianScalarProduct[p, q, Dimension -> D - 1] // StandardForm
(*CartesianPair[CartesianMomentum[p, -1 + D], CartesianMomentum[q, -1 + D]]*)CartesianScalarProduct[Subscript[p, 1], Subscript[p, 2]] = s/2\frac{s}{2}
ExpandScalarProduct[ CartesianScalarProduct[Subscript[p, 1] - q, Subscript[p, 2] - k]]-\overline{k}\cdot \overline{p}_1+\overline{k}\cdot \overline{q}-\overline{q}\cdot \overline{p}_2+\frac{s}{2}
Calc[ CartesianScalarProduct[Subscript[p, 1] - q, Subscript[p, 2] - k]]-\overline{k}\cdot \overline{p}_1+\overline{k}\cdot \overline{q}-\overline{q}\cdot \overline{p}_2+\frac{s}{2}
CartesianScalarProduct[q1] = qq;CSP[q1]\text{qq}
FCClearScalarProducts[]