CLC[m, n, r]
evaluates to
Eps[CartesianIndex[m], CartesianIndex[n], CartesianIndex[r]]
applying FeynCalcInternal
.
CLC[m,...][p, ...]
evaluates to
Eps[CartesianIndex[m], ..., CartesianMomentum[p], ...]
applying FeynCalcInternal
.
When some indices of a Levi-Civita-tensor are contracted with
3-vectors, FeynCalc suppresses explicit dummy indices by putting those
vectors into the corresponding index slots. For example, \varepsilon^{p_1 p_2 p_3} (accessible via
CLC[][p1,p2,p3]
) correspond to \varepsilon^{i j k} p_1^i p_2^j p_3^k.
[i, j, k] CLC
\bar{\epsilon }^{ijk}
[i, j, k] // FCI // StandardForm
CLC
(*Eps[CartesianIndex[i], CartesianIndex[j], CartesianIndex[k]]*)
[i][p, q] CLC
\bar{\epsilon }^{i\overline{p}\overline{q}}
[i][p, q] // FCI // StandardForm
CLC
(*Eps[CartesianIndex[i], CartesianMomentum[p], CartesianMomentum[q]]*)
[CLC[i, j, k] CLC[i, l, m]] Contract
\bar{\delta }^{jl} \bar{\delta }^{km}-\bar{\delta }^{jm} \bar{\delta }^{kl}
[i, j, k] CV[Subscript[p, 1], i] CV[Subscript[p, 2], j] CV[Subscript[p, 3], k]
CLC
[%] Contract
\overline{p}_1{}^i \overline{p}_2{}^j \overline{p}_3{}^k \bar{\epsilon }^{ijk}
\bar{\epsilon }^{\overline{p}_1\overline{p}_2\overline{p}_3}