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| -rw-r--r-- | marginal.tex | 10 |
1 files changed, 5 insertions, 5 deletions
diff --git a/marginal.tex b/marginal.tex index c8d0b8b..88809d2 100644 --- a/marginal.tex +++ b/marginal.tex @@ -1802,13 +1802,13 @@ 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 $\mathbf e(1)=\{1,i\bar\theta_1\theta_1\}$ 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 $\mathbf -f(1)=\{i\bar\theta_1,i\theta_1\}$ is that of the odd subspace, dual bases $\mathbf e^\dagger(1)=\{i\bar\theta_1\theta_1,1\}$ and $\mathbf f^\dagger(1)=\{-\theta_1,\bar\theta_1\}$ can be defined by the requirement that +f(1)=\{\bar\theta_1,\theta_1\}$ is that of the odd subspace, dual bases $\mathbf e^\dagger(1)=\{\bar\theta_1\theta_1,1\}$ and $\mathbf f^\dagger(1)=\{-\theta_1,\bar\theta_1\}$ can be defined by the requirement that \begin{align} - &\int d1\,e_i^\dagger(1)e_j(1)=i\delta_{ij} + &\int d1\,e_i^\dagger(1)e_j(1)=\delta_{ij} && - \int d1\,f_i^\dagger(1)f_j(1)=i\delta_{ij} \\ + \int d1\,f_i^\dagger(1)f_j(1)=\delta_{ij} \\ &\int d1\,e_i^\dagger(1)f_j(1)=0 && \int d1\,f_i^\dagger(1)e_j(1)=0 @@ -1825,7 +1825,7 @@ block representation of $M$ in analogy to the matrix form of an operator in quan & \mathbf f^\dagger(1)M(1,2)\mathbf f(2) \end{bmatrix} - =i\begin{bmatrix} + =\begin{bmatrix} A & B \\ C & D \end{bmatrix} \end{equation} |