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[]