Theory and Modern Applications
Table 2 Commutator table after optimization
\([ \boldsymbol{V}_{\boldsymbol{1}}, \boldsymbol{V}_{\boldsymbol{2}}]\) | \(\boldsymbol{X}_{\boldsymbol{1}}\) | \(\boldsymbol{X}_{\boldsymbol{2}}\) | \(\boldsymbol{X}_{\boldsymbol{3}}\) | \(\boldsymbol{X}_{\boldsymbol{4}}\) |
|---|---|---|---|---|
\(\boldsymbol{X}_{\boldsymbol{1}}\) | 0 | 0 | \(\boldsymbol{X}_{\boldsymbol{1}}\) | 0 |
\(\boldsymbol{X}_{\boldsymbol{2}}\) | 0 | 0 | \(-2 \boldsymbol{X}_{\boldsymbol{2}}\) | \(4 \boldsymbol{X}_{\boldsymbol{2}}\) |
\(\boldsymbol{X}_{\boldsymbol{3}}\) | \(- \boldsymbol{X}_{\boldsymbol{1}}\) | \(2 \boldsymbol{X}_{\boldsymbol{2}}\) | 0 | 0 |
\(\boldsymbol{X}_{\boldsymbol{4}}\) | 0 | \(-4 \boldsymbol{X}_{\boldsymbol{2}}\) | 0 | 0 |