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