Noncommutative geometry and the BV formalism: application to a U(2)-matrix model

In recent years noncommutative geometry has given proof of being an
interesting setting for the analysis of gauge theories. The reason 
has to be searched in the fact that noncommutative manifolds naturally
induce gauge theories. It is then reasonable to try to insert in this
setting also procedures which have been developed for the analysis 
of gauge theories, such as the BV approach to the BRST quantization 
of non-abelian gauge theories.

In this talk we concetrate on a matrix model with a U(2)-gauge 
symmetry and we present a method to incorporate the BV construction
in the framework of noncommutative geometry. This is done via the 
introduction of a BV-spectral triple. 

The interesting aspect of this approach is that the ghost fields,
which play a fundamental role in the BV construction, as well as
all their physical properties can be interpreted in terms of the
structure of the spectral triple.