FeynCalc manual (development version)

PauliTrace

PauliTrace[exp] is the head of Pauli traces. By default the trace is not evaluated. The evaluation occurs only when the option PauliTraceEvaluate is set to True. It is recommended to use PauliSimplify, which will automatically evaluate all Pauli traces in the input expression.

See also

Overview, PauliSimplify.

Examples

PauliTrace[CSI[i, j, k, l]]

tr(σ‾i.σ‾j.σ‾k.σ‾l)\text{tr}\left(\overline{\sigma }^i.\overline{\sigma }^j.\overline{\sigma }^k.\overline{\sigma }^l\right)

PauliTrace[CSI[i, j, k, l], PauliTraceEvaluate -> True]

2(δˉilδˉjk−δˉikδˉjl+δˉijδˉkl)2 \left(\bar{\delta }^{il} \bar{\delta }^{jk}-\bar{\delta }^{ik} \bar{\delta }^{jl}+\bar{\delta }^{ij} \bar{\delta }^{kl}\right)

PauliTrace[CSI[i, j, k, l]] 
 
% // PauliSimplify

tr(σ‾i.σ‾j.σ‾k.σ‾l)\text{tr}\left(\overline{\sigma }^i.\overline{\sigma }^j.\overline{\sigma }^k.\overline{\sigma }^l\right)

2δˉilδˉjk−2δˉikδˉjl+2δˉijδˉkl2 \bar{\delta }^{il} \bar{\delta }^{jk}-2 \bar{\delta }^{ik} \bar{\delta }^{jl}+2 \bar{\delta }^{ij} \bar{\delta }^{kl}