- Can somebody share a link to papers( books) where this fornula was deduced? $e^{\frac{1}{2}\sum_{ij}K_{ij}s_is_j} =\left(\frac{\det{K}}{(2\pi)^N} \right)^{1/2} \int^{\infty}_{-\infty}...\int^{\infty}_{\infty}\prod_{k=1}^Nd\phi_k \exp{\left[-\frac{1}{2}\sum_{ij}\phi_i K_{ij}\phi_j + \sum_{ij} s_iK_{ij}\phi_j\right]}$
where $K$ is a symmetric positive definite matrix 2. What is if K is negative? I think the following $e^{\frac{1}{2}\sum_{ij}(-|K_{ij}|s_is_j)} =\left(\frac{\det{K}}{(2\pi)^N} \right)^{1/2} \int^{\infty}_{-\infty}...\int^{\infty}_{\infty}\prod_{k=1}^Nd\phi_k \exp{\left[-\frac{1}{2}\sum_{ij}\phi_i K_{ij}\phi_j + i\sum_{ij} s_iK_{ij}\phi_j\right]}$
