FeynCalc manual (development version)

CartesianMomentum

CartesianMomentum[p] is the head of a 3-momentum p. The internal representation of a 3-dimensional p is CartesianMomentum[p]. For other than three dimensions: CartesianMomentum[p, Dimension]. CartesianMomentum[p, 3] simplifies to CartesianMomentum[p].

See also

Overview, Momentum, TemporalMomentum.

Examples

This is a 3-dimensional momentum

CartesianMomentum[p]

\overline{p}

As an optional second argument the dimension must be specified if it is different from 3

CartesianMomentum[p, D - 1]

p

The dimension index is suppressed in the output.

CartesianMomentum[p, d - 1]

p

a1 = CartesianMomentum[-q]

-\overline{q}

a1 // StandardForm

(*-CartesianMomentum[q]*)

a2 = CartesianMomentum[p - q] + CartesianMomentum[2 q]

\left(\overline{p}-\overline{q}\right)+2 \overline{q}

a2 // StandardForm

(*CartesianMomentum[p - q] + 2 CartesianMomentum[q]*)

a2 // MomentumExpand // StandardForm

(*CartesianMomentum[p] + CartesianMomentum[q]*)

a2 // MomentumCombine // StandardForm

(*CartesianMomentum[p + q]*)

Notice that when changing the dimension, one must specify its value as if the the 3-vector were the spatial component of the corresponding 4-vector

ChangeDimension[CartesianMomentum[p], d - 1] // StandardForm

(*CartesianMomentum[p, -2 + d]*)

ChangeDimension[CartesianMomentum[p], d] // StandardForm

(*CartesianMomentum[p, -1 + d]*)

Clear[a1, a2]