Giovanni Sparano

Learn More
In this paper we study the structure of the Hilbert space for the recent noncommutative geometry models of gauge theories. We point out the presence of unphysical degrees of freedom similar to the ones appearing in lattice gauge theories (fermion doubling). We investigate the possibility of projecting out these states at the various levels in the(More)
The solutions of vacuum Einstein's field equations, for the class of Riemannian metrics admitting a non Abelian bidimensional Lie algebra of Killing fields, are explicitly described. They are parametrized either by solutions of a transcendental equation (the tortoise equation), or by solutions of a linear second order differential equation in two(More)
The Connes and Lott reformulation of the strong and electroweak model represents a promising application of noncommutative geometry. In this scheme the Higgs field naturally appears in the theory as a particular gauge boson, connected to the discrete internal space, and its quartic potential, fixed by the model, is not vanishing only when more than one(More)
Conventional discrete approximations of a manifold do not preserve its nontrivial topological features. In this article we describe an approximation scheme due to Sorkin which reproduces physically important aspects of manifold topology with striking delity. The approximating topological spaces in this scheme are partially ordered sets (posets). Now, in(More)
Geometric structures underlying commutative and non commutative integrable dynamics are analyzed. They lead to a new characterization of noncommutative integrability in terms of spectral properties and of Nijenhuis torsion of an invariant (1,1) tensor field. The construction of compatible symplectic structures is also discussed. Subj. Class.: Dynamical(More)
We discuss several aspects of singularities of the solutions of the partial differential equations of Klein–Gordon, Schrödinger and Dirac. In particular we analyze the fold type singularity, of the first and higher orders, and the related characteristic equations. We also consider the field equations as reduction of homogenous equations in higher(More)
We consider finite approximations of a topological space M by noncommutative lattices of points. These lattices are structure spaces of noncommutativeC∗-algebras which in turn approximate the algebra C(M) of continuous functions on M . We show how to recover the space M and the algebra C(M) from a projective system of noncommutative lattices and an(More)