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| -rw-r--r-- | marginal.tex | 13 |
1 files changed, 11 insertions, 2 deletions
diff --git a/marginal.tex b/marginal.tex index 88809d2..85743c3 100644 --- a/marginal.tex +++ b/marginal.tex @@ -1843,8 +1843,17 @@ The same method can be used to calculate the superdeterminant and supertrace in arbitrary superspaces, where for $\mathbb R^{N|2D}$ each basis has $2^{2D-1}$ elements. For instance, for $\mathbb R^{N|4}$ we have \begin{align} - &\mathbf e(1,2)=\{1,i\bar\theta_1\theta_1,i\bar\theta_2\theta_2,i\bar\theta_1\theta_2,i\bar\theta_2\theta_1,i\bar\theta_1\bar\theta_2,i\theta_1\theta_2,\bar\theta_1\theta_1\bar\theta_2\theta_2\}\notag \\ - &\mathbf f(1,2)=\{i\bar\theta_1,i\theta_1,i\bar\theta_2,i\theta_2,\bar\theta_1\theta_1\bar\theta_2,\bar\theta_2\theta_2\theta_1,\bar\theta_1\theta_1\theta_2,\bar\theta_2\theta_2\theta_1\} + &\mathbf e(1,2)=\{ + 1,\bar\theta_1\theta_1,\bar\theta_2\theta_2, + \bar\theta_1\theta_2,\bar\theta_2\theta_1, + \bar\theta_1\bar\theta_2,\theta_1\theta_2, + \bar\theta_1\theta_1\bar\theta_2\theta_2 + \}\notag \\ + &\mathbf f(1,2)=\{ + \bar\theta_1,\theta_1,\bar\theta_2,\theta_2, + \bar\theta_1\theta_1\bar\theta_2,\bar\theta_2\theta_2\theta_1, + \bar\theta_1\theta_1\theta_2,\bar\theta_2\theta_2\theta_1 + \} \end{align} with the dual bases defined analogously to those above. |