  This paper aims to give a probabilistic construction of interactions which
may be relevant for building physical theories such as interacting quantum
field theories. We start with the path integral definition of partition
function in quantum field theory which recall us the probabilistic nature of
this physical theory. From a Gaussian law considered as free theory, an
interacting theory is constructed by nontrivial convolution product between the
free theory and an interacting term which is also a probability law. The
resulting theory, again a probability law, exhibits two proprieties already
present in nowadays theories of interactions such as Gauge theory : the
interaction term does not depend on the free term, and two different free
theories can be implemented with the same interaction. The direct use of
Gaussian measures allows to generalize the present construction for infinite
dimensional spaces equipped with Gaussian measures.
