Hi all! I want to perturbatively solve this equation in \beta at second order in \alpha
\frac{\beta^{2}}{4}-\frac{3}{8}\beta^{4}\alpha+\frac{2}{3}\beta^{6}\alpha^{2}=\frac{1}{4}
I rewrite this formula in this way
\beta^{2}=1+\frac{3}{2}\beta^{4}\alpha-\frac{8}{3}\beta^{6}\alpha^{2}...
Thank you very much. I have fixed this problem by simply rescale x_i with \sqrt \epsilon. this makes \epsilon disappear from any fraction and the structure of even powers of the polynomial makes everything analytical and taylor expandeable.
The idea of the steepest descent method is a smart...
Hi everyone. The problem I have to face is to perform a taylor series expansion of the integral
\int_{-\infty}^{\infty}\frac{e^{-\sum_{i}\frac{x_{i}^{2}}{2\epsilon}}}{\sqrt{2\pi\epsilon}^{N}}\cdot e^{f(\{x\})}dx_{i}\ldots dx_{N}
with respect to variance \epsilon. I find some difficulties...