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
FCTP[a, b, c]
% // StandardForm\overline{a}\cdot \left(\overline{b}\times \overline{c}\right)
(*FCTripleProduct[a, b, c]*)FCTP[a, b, c, Explicit -> True]
% // StandardForm\bar{\epsilon }^{\overline{a}\overline{b}\overline{c}}
(*Eps[CartesianMomentum[a], CartesianMomentum[b], CartesianMomentum[c]]*)FCTP[QuantumField[A, CartesianIndex[i]], QuantumField[B, CartesianIndex[j]],
QuantumField[C, CartesianIndex[k]], Explicit -> True]\bar{\epsilon }^{ijk} A^i.B^j.C^k
FCTP[a, b, c, Explicit -> True, NonCommutative -> True, CartesianIndexNames -> {i, j, k}]\bar{\epsilon }^{ijk} \overline{a}^i.\overline{b}^j.\overline{c}^k