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| author | Jaron Kent-Dobias <jaron@kent-dobias.com> | 2024-10-29 10:24:54 +0100 |
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| committer | Jaron Kent-Dobias <jaron@kent-dobias.com> | 2024-10-29 10:24:54 +0100 |
| commit | f824dea3df7492fecfa95d34b33900a533bfd699 (patch) | |
| tree | 74560807522c9f2ba7f973a29b2ad9b39cf0ac8b /marginal.tex | |
| parent | 568324cd4bc0cf2dd6a81464b1c4c700ee7ebfa5 (diff) | |
| download | marginal-f824dea3df7492fecfa95d34b33900a533bfd699.tar.gz marginal-f824dea3df7492fecfa95d34b33900a533bfd699.tar.bz2 marginal-f824dea3df7492fecfa95d34b33900a533bfd699.zip | |
Changed also convention for superbasis in R^N|4
Diffstat (limited to 'marginal.tex')
| -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. |