FeynCalc manual (development version)

CGA

CGA[i] can be used as input for γi\gamma^i in 4 dimensions, where i is a Cartesian index, and is transformed into DiracGamma[CartesianIndex[i]] by FeynCalcInternal.

See also

Overview, GA, DiracGamma.

Examples

CGA[i]

γi\overline{\gamma }^i

CGA[i, j] - CGA[j, i]

γi.γjγj.γi\overline{\gamma }^i.\overline{\gamma }^j-\overline{\gamma }^j.\overline{\gamma }^i

StandardForm[FCI[CGA[i]]]

(*DiracGamma[CartesianIndex[i]]*)
CGA[i, j, k, l]

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

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

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

4δˉilδˉjk4δˉikδˉjl+4δˉijδˉkl4 \bar{\delta }^{il} \bar{\delta }^{jk}-4 \bar{\delta }^{ik} \bar{\delta }^{jl}+4 \bar{\delta }^{ij} \bar{\delta }^{kl}

CGA[i] . (CGS[p] + m) . CGA[j]

γi.(γp+m).γj\overline{\gamma }^i.\left(\overline{\gamma }\cdot \overline{p}+m\right).\overline{\gamma }^j