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 CartesianScalarProduct
s before any calculation. This improves the performance of FeynCalc.
[p, q] CartesianScalarProduct
[p + q, -q] CartesianScalarProduct
[p, p] CartesianScalarProduct
[q] CartesianScalarProduct
[p, q] // StandardForm
CartesianScalarProduct
(*CartesianPair[CartesianMomentum[p], CartesianMomentum[q]]*)
[p, q, Dimension -> D - 1] // StandardForm
CartesianScalarProduct
(*CartesianPair[CartesianMomentum[p, -1 + D], CartesianMomentum[q, -1 + D]]*)
[Subscript[p, 1], Subscript[p, 2]] = s/2 CartesianScalarProduct
[ CartesianScalarProduct[Subscript[p, 1] - q, Subscript[p, 2] - k]] ExpandScalarProduct
[ CartesianScalarProduct[Subscript[p, 1] - q, Subscript[p, 2] - k]] Calc
[q1] = qq; CartesianScalarProduct
[q1] CSP
[] FCClearScalarProducts