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Let $B=(B_1(t),..,B_d(t))$ be a $d$-dimensional fractional Brownian motionwith Hurst index $\alpha\le 1/4$, or more generally a Gaussian process whosepaths have the same local regularity. Defining properly iterated integrals of$B$ is a difficult task because of the low H\"older regularity index of itspaths. Yet rough path theory shows it is the key to the construction of astochastic calculus with respect to $B$, or to solving differential equationsdriven by $B$. We intend to show in a forthcoming series of papers how todesingularize iterated integrals by a weak singular non-Gaussian perturbationof the Gaussian measure defined by a limit in law procedure.  Convergence is proved by using "standard" tools of constructive field theory,in particular cluster expansions and renormalization. These powerful toolsallow optimal estimates of the moments and call for an extension of theGaussian tools such as for instance the Malliavin calculus. This first paperaims to be both a presentation of the basics of rough path theory tophysicists, and of perturbative field theory to probabilists; it is onlyheuristic, in particular because the desingularization of iterated integrals isreally a {\em non-perturbative} effect. It is also meant to be a generalmotivating introduction to the subject, with some insights into quantum fieldtheory and stochastic calculus. The interested reader should read in a secondtime the companion article \cite{MagUnt2} (or a preliminary versionarXiv:1006.1255) for the constructive proofs.

From constructive field theory to fractional stochastic calculus. (I) An introduction: rough path theory and perturbative heuristics