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| -rw-r--r-- | marginal.tex | 4 |
1 files changed, 2 insertions, 2 deletions
diff --git a/marginal.tex b/marginal.tex index 024b0ac..95955b5 100644 --- a/marginal.tex +++ b/marginal.tex @@ -982,7 +982,7 @@ $f$ is an arbitrary function, then \end{equation} This kind of behavior of integrals over the Grassmann indices makes them useful for compactly expressing the Kac--Rice measure. To see why, consider the -specific superspace $\mathbb R^{N|2}$, where an arbitrary vector can be expression as +specific superspace $\mathbb R^{N|2}$, where an arbitrary vector can be expressed as \begin{equation} \pmb\phi(1)=\mathbf x+\bar\theta_1\pmb\eta+\bar{\pmb\eta}\theta_1+\bar\theta_1\theta_1i\hat{\mathbf x} \end{equation} @@ -1038,7 +1038,7 @@ Integrals involving superfields contracted into such operators result in schemat \end{equation} where the usual role of the determinant is replaced by the superdeterminant. The superdeterminant can be defined using the ordinary determinant by writing a -block version of the matrix $M$: if $\mathbf e(1)=\{1,\bar\theta_1\theta\}$ is +block version of the matrix $M$: if $\mathbf e(1)=\{1,\bar\theta_1\theta_1\}$ is the basis vector of the even subspace of the superspace and $\mathbf f(1)=\{\bar\theta_1,\theta_1\}$ is that of the odd subspace, then we can form a block representation of $M$ in analogy to the matrix form of an operator in quantum mechanics by |