Résumé :
We consider the topological quantum field theory properties of sutured Floer homology, as introduced by Honda--Kazez--Matic. We present several results in the ``dimensionally reduced" case of product manifolds. The SFH of such manifolds reduces to that of solid tori, and forms a ``categorification of Pascal's triangle". Contact
structures correspond to chord diagrams, and contact elements form
distinguished subsets of SFH of order given by the Catalan numbers. We find natural ``creation and annihilation operators'' which allow us to define a QFT-type basis of SFH, consisting of contact elements. In fact sutured Floer homology in this case reduces to the combinatorics
of chord diagrams, and in a sense which can be made precise, is the
``quantum field theory of two non-commuting particles". The details of
this description have intrinsic contact-topological meaning, allowing
us for instance to compute certain contact categories, and to give a
``contact geometry free" proof that the contact element of a contact
structure with torsion is zero.