Paths with singularities in functional integrals of quantum field theory
  In the toy model ($ \phi^{4}$-interacting quantum field theory in one-dimensional "Euclidean" space-time) we prove that the functional integrals of the free field theory evaluated over the space of continuous functions are equal to the functional integrals of the interacting field theory evaluated over a set of spaces containing the spaces of discontinuous functions. 
V.V. Belokurov and E.T. Shavgulidze
hep-th math-ph math.MP