FCTripleProduct[a,b,c]
returns the triple product a \cdot (b \times c). By default a
,b
and c
are assumed to be Cartesian vectors. Wrapping the arguments with CartesianIndex
will create an expression with open indices.
If any of the arguments is noncommutative, DOT
will be used instead of Times
and the function will introduce dummy indices. To give those indices some specific names, use the option CartesianIndexNames
.
If the arguments already contain free CartesianIndices, the first such index will be used for the contraction.
To obtain an explicit expression you need to set the option Explicit
to True
or apply the function Explicit
[a, b, c]
FCTP
% // StandardForm
\overline{a}\cdot \left(\overline{b}\times \overline{c}\right)
(*FCTripleProduct[a, b, c]*)
[a, b, c, Explicit -> True]
FCTP
% // StandardForm
\bar{\epsilon }^{\overline{a}\overline{b}\overline{c}}
(*Eps[CartesianMomentum[a], CartesianMomentum[b], CartesianMomentum[c]]*)
[QuantumField[A, CartesianIndex[i]], QuantumField[B, CartesianIndex[j]],
FCTP[C, CartesianIndex[k]], Explicit -> True] QuantumField
\bar{\epsilon }^{ijk} A^i.B^j.C^k
[a, b, c, Explicit -> True, NonCommutative -> True, CartesianIndexNames -> {i, j, k}] FCTP
\bar{\epsilon }^{ijk} \overline{a}^i.\overline{b}^j.\overline{c}^k