  Let $B=(B_1(t),..,B_d(t))$ be a $d$-dimensional fractional Brownian motion
with Hurst index $\alpha\le 1/4$, or more generally a Gaussian process whose
paths have the same local regularity. Defining properly iterated integrals of
$B$ is a difficult task because of the low H\"older regularity index of its
paths. Yet rough path theory shows it is the key to the construction of a
stochastic calculus with respect to $B$, or to solving differential equations
driven by $B$. We intend to show in a forthcoming series of papers how to
desingularize iterated integrals by a weak singular non-Gaussian perturbation
of 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 tools
allow optimal estimates of the moments and call for an extension of the
Gaussian tools such as for instance the Malliavin calculus. This first paper
aims to be both a presentation of the basics of rough path theory to
physicists, and of perturbative field theory to probabilists; it is only
heuristic, in particular because the desingularization of iterated integrals is
really a {\em non-perturbative} effect. It is also meant to be a general
motivating introduction to the subject, with some insights into quantum field
theory and stochastic calculus. The interested reader should read in a second
time the companion article \cite{MagUnt2} (or a preliminary version
arXiv:1006.1255) for the constructive proofs.
