CartesianPair[a, b]
is a special pairing used in the internal representation. a
and b
may have heads CartesianIndex
or CartesianMomentum
. If both a
and b
have head CartesianIndex
, the Kronecker delta is understood. If a
and b
have head CartesianMomentum
, a Cartesian scalar product is meant. If one of a
and b
has head CartesianIndex
and the other CartesianMomentum
, a Cartesian vector is understood.
This represents a three-dimensional Kronecker delta
[CartesianIndex[i], CartesianIndex[j]] CartesianPair
This is a -dimensional Kronecker delta
[CartesianIndex[i, D - 1], CartesianIndex[j, D - 1]] CartesianPair
If the Cartesian indices live in different dimensions, this gets resolved according to the t’Hoft-Veltman-Breitenlohner-Maison prescription
[CartesianIndex[i, D - 1], CartesianIndex[j]] CartesianPair
[CartesianIndex[i, D - 1], CartesianIndex[j, D - 4]] CartesianPair
[CartesianIndex[i], CartesianIndex[j, D - 4]] CartesianPair
A -dimensional Cartesian vector
[CartesianIndex[i], CartesianMomentum[p]] CartesianPair
A -dimensional Cartesian vector
[CartesianIndex[i, D - 1], CartesianMomentum[p, D - 1]] CartesianPair
-dimensional scalar products of Cartesian vectors
[CartesianMomentum[q], CartesianMomentum[p]] CartesianPair
[CartesianMomentum[p], CartesianMomentum[p]] CartesianPair
[CartesianMomentum[p - q], CartesianMomentum[p]] CartesianPair
[CartesianMomentum[p], CartesianMomentum[p]]^2 CartesianPair
[CartesianMomentum[p], CartesianMomentum[p]]^3 CartesianPair
[CartesianPair[CartesianMomentum[p - q], CartesianMomentum[p]]] ExpandScalarProduct
[CartesianMomentum[-q], CartesianMomentum[p]] +
CartesianPair[CartesianMomentum[q], CartesianMomentum[p]] CartesianPair