  The Wiener Sausage, the volume traced out by a sphere attached to a Brownian
particle, is a classical problem in statistics and mathematical physics.
Initially motivated by a range of field-theoretic, technical questions, we
present a single loop renormalised perturbation theory of a stochastic process
closely related to the Wiener Sausage, which, however, proves to be exact for
the exponents and some amplitudes. The field-theoretic approach is particularly
elegant and very enjoyable to see at work on such a classic problem. While we
recover a number of known, classical results, the field-theoretic techniques
deployed provide a particularly versatile framework, which allows easy
calculation with different boundary conditions even of higher momenta and more
complicated correlation functions. At the same time, we provide a highly
instructive, non-trivial example for some of the technical particularities of
the field-theoretic description of stochastic processes, such as excluded
volume, lack of translational invariance and immobile particles. The aim of the
present work is not to improve upon the well-established results for the Wiener
Sausage, but to provide a field-theoretic approach to it, in order to gain a
better understanding of the field-theoretic obstacles to overcome.
