  In this work, we have studied classical and quantum systems in interaction by
means of geometric reduction procedure. The main target is the description in
these terms of fundamental interactions. We have shown that, to describe in a
canonical way (i.e., in terms of Poisson/Dirac Brackets) even a simple system
like the relativistic free particle, one has to deal with non-commutative
positions. We have explored some consequences of this result in the framework
of Non-Commutative Geometry and in Quantum Gravity.
