FeynCalc manual (development version)

CGAD

CGAD[i] can be used as input for γi\gamma ^i in DD dimensions, where i is a Cartesian index, and is transformed into DiracGamma[CartesianIndex[i,D-1],D] by FeynCalcInternal.

See also

Overview, GAD, DiracGamma.

Examples

CGAD[i]

γi\gamma ^i

CGAD[i, j] - CGAD[j, i]

γi.γjγj.γi\gamma ^i.\gamma ^j-\gamma ^j.\gamma ^i

StandardForm[FCI[CGAD[i]]]

(*DiracGamma[CartesianIndex[i, -1 + D], D]*)
CGAD[i, j, k, l]

γi.γj.γk.γl\gamma ^i.\gamma ^j.\gamma ^k.\gamma ^l

StandardForm[CGAD[i, j, k, l]]

(*CGAD[i] . CGAD[j] . CGAD[k] . CGAD[l]*)
DiracSimplify[DiracTrace[CGAD[i, j, k, l]]]

4δilδjk4δikδjl+4δijδkl4 \delta ^{il} \delta ^{jk}-4 \delta ^{ik} \delta ^{jl}+4 \delta ^{ij} \delta ^{kl}

CGAD[i] . (CGSD[p] + m) . CGAD[j]

γi.(m+γp).γj\gamma ^i.(m+\gamma \cdot p).\gamma ^j