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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 theâ€¦ (More)

Using the tools of noncommutative geometry we calculate the distances between the points of a lattice on which the usual discretized Dirac operator has been defined. We find that these distances do not have the expected behaviour, revealing that from the metric point of view the lattice does not look at all as a set of points sitting on the continuumâ€¦ (More)

- Giovanni Sparano, G. Vilasi, Alexandre M. Vinogradov

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 twoâ€¦ (More)

- Giovanni Sparano
- 2008

Vacuum gravitational fields invariant for a bidimensional non Abelian Lie algebra of Killing fields, are explicitly described. They are parameterized either by solutions of a transcendental equation (the tortoise equation) or by solutions of a linear second order differential equation on the plane. Gravitational fields determined via the tortoise equation,â€¦ (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 oneâ€¦ (More)

Quantum Groups can be constructed by applying the quantization by deformation procedure to Lie groups endowed with a suitable Poisson bracket. Here we try to develop an understanding of these structures by investigating dynamical systems which are associated with this bracket. We look at SU (2) and SU (1, 1), as submanifolds of a 4â€“dimensional phase spaceâ€¦ (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, inâ€¦ (More)

- Giovanni Sparano, G. Vilasi
- 1999

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.: Dynamicalâ€¦ (More)

We discuss several aspects of singularities of the solutions of the partial differential equations of Kleinâ€“Gordon, SchrÃ¶dinger 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 higherâ€¦ (More)

We consider finite approximations of a topological space M by noncommutative lattices of points. These lattices are structure spaces of noncommutativeCâˆ—-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 anâ€¦ (More)