ScalarProduct

Description

ScalarProduct[p, q] is the input for scalar product. ScalarProduct[p] is equivalent to ScalarProduct[p, p]. Expansion of sums of momenta in ScalarProduct is done with ExpandScalarProduct. Scalar product may be set, e.g., ScalarProduct[a, b] = m^2; but a and b must not contain sums. Note that ScalarProduct[a, b] = m^2 actually sets also: Pair[Momentum[a, ___], Momentum[b, ___]] = m^2. It is encouraged to always set ScalarProduct's before any calculation. This improves the performance of FeynCalc .

See also: Calc, ClearScalarProducts, ExpandScalarProduct, Pair, SP, SPD.

Examples

ScalarProduct[p, q]

ScalarProduct[p + q, -q]

ScalarProduct[p, p]

ScalarProduct[q]

ScalarProduct[p, q] // StandardForm

ScalarProduct[p, q, Dimension -> D] // StandardForm

ScalarProduct[(Subscript[p, 1]), (Subscript[p, 2])]  =  s/2

ExpandScalarProduct[ ScalarProduct[(Subscript[p, 1]) - q, (Subscript[p, 2]) - k]]

Calc[ ScalarProduct[(Subscript[p, 1]) - q, (Subscript[p, 2]) - k]]

ClearScalarProducts