FeynCalc manual (development version)

PauliSigma

PauliSigma[x, dim] is the internal representation of a Pauli matrix with a Lorentz or Cartesian index or a contraction of a Pauli matrix and a Lorentz or Cartesian vector.

PauliSigma[x,3] simplifies to PauliSigma[x].

See also

Overview, SI, CSI.

Examples

PauliSigma[LorentzIndex[\[Alpha]]]

\bar{\sigma }^{\alpha }

PauliSigma[CartesianIndex[i]]

\overline{\sigma }^i

A Pauli matrix contracted with a Lorentz or Cartesian vector is displayed as \sigma \cdot p

PauliSigma[Momentum[p]]

\bar{\sigma }\cdot \overline{p}

PauliSigma[CartesianMomentum[p]]

\overline{\sigma }\cdot \overline{p}

PauliSigma[Momentum[q]] . PauliSigma[Momentum[p - q]] 
 
% // PauliSigmaExpand

\left(\bar{\sigma }\cdot \overline{q}\right).\left(\bar{\sigma }\cdot \left(\overline{p}-\overline{q}\right)\right)

\left(\bar{\sigma }\cdot \overline{q}\right).\left(\bar{\sigma }\cdot \overline{p}-\bar{\sigma }\cdot \overline{q}\right)

PauliSigma[CartesianMomentum[q]] . PauliSigma[CartesianMomentum[p - q]] 
 
% // PauliSigmaExpand

\left(\overline{\sigma }\cdot \overline{q}\right).\left(\overline{\sigma }\cdot \left(\overline{p}-\overline{q}\right)\right)

\left(\overline{\sigma }\cdot \overline{q}\right).\left(\overline{\sigma }\cdot \overline{p}-\overline{\sigma }\cdot \overline{q}\right)