1206.5319 (Theo Johnson-Freyd)

Homological perturbation theory for nonperturbative integrals    [PDF]

Theo Johnson-Freyd

In this paper we study integrals of the form $\int_{\gamma}fe^{s}$, where $f$ and $s$ are complex polynomials of $n$ variables and $\gamma\subseteq \CC^{n}$ is an $n$-real-dimensional contour along which $e^{s}$ enjoys exponential decay. Suppose $s$ is generic of degree $d$. Using homological algebra, we automate the method of "integration by parts," and show how to express any such integral as a linear combination of integrals of monomials which are of degree $View original: http://arxiv.org/abs/1206.5319