FeynCalc manual (development version)

CLCD

CLCD[m, n, r] evaluates to Eps[CartesianIndex[m, D-1], CartesianIndex[n, D-1], CartesianIndex[r,D-1]] applying FeynCalcInternal.

CLC[m,...][p, ...] evaluates to Eps[CartesianIndex[m, D-1], ..., CartesianMomentum[p, D-1], ...] 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 CLCD[][p1,p2,p3]) correspond to \varepsilon^{i j k} p_1^i p_2^j p_3^k.

See also

Overview, LCD, Eps.

Examples

CLCD[i, j, k]

\overset{\text{}}{\epsilon }^{ijk}

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

(*Eps[CartesianIndex[i, -1 + D], CartesianIndex[j, -1 + D], CartesianIndex[k, -1 + D]]*)

CLCD[i, j][p]

\overset{\text{}}{\epsilon }^{ijp}

CLCD[i, j][p] // FCI // StandardForm

(*Eps[CartesianIndex[i, -1 + D], CartesianIndex[j, -1 + D], CartesianMomentum[p, -1 + D]]*)

CLCD[i, j][p] CLCD[i, j][q] // Contract // Factor2

(2-D) (3-D) (p\cdot q)

CLCD[i, j, k] CVD[Subscript[p, 1], i] CVD[Subscript[p, 2], j] CVD[Subscript[p, 3], k] 
 
Contract[%]

p_1{}^i p_2{}^j p_3{}^k \overset{\text{}}{\epsilon }^{ijk}

\overset{\text{}}{\epsilon }^{p_1p_2p_3}