FeynCalc manual (development version)

FCTripleProduct

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

See also

Overview, Eps.

Examples

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}]

$$\bar{\epsilon }^{ijk} \overline{a}^i.\overline{b}^j.\overline{c}^k$$