FeynCalc manual (development version)

CLC

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.

See also

Overview, LC, Eps.

Examples

CLC[i, j, k]

\bar{\epsilon }^{ijk}

CLC[i, j, k] // FCI // StandardForm

(*Eps[CartesianIndex[i], CartesianIndex[j], CartesianIndex[k]]*)
CLC[i][p, q]

\bar{\epsilon }^{i\overline{p}\overline{q}}

CLC[i][p, q] // FCI // StandardForm

(*Eps[CartesianIndex[i], CartesianMomentum[p], CartesianMomentum[q]]*)
Contract[CLC[i, j, k] CLC[i, l, m]]

\bar{\delta }^{jl} \bar{\delta }^{km}-\bar{\delta }^{jm} \bar{\delta }^{kl}

CLC[i, j, k] CV[Subscript[p, 1], i] CV[Subscript[p, 2], j] CV[Subscript[p, 3], k] 
 
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}