51 citations · 597 across the 45 of their papers we have counts for
8 papers · 1 filter
The Standard Model in noncommutative geometry: fundamental fermions as internal forms
Ludwik Dabrowski, Francesco D'Andrea, Andrzej Sitarz
Given the algebra, Hilbert space H, grading and real structure of the finite spectral triple of the Standard Model, we classify all possible Dirac operators such that H is a self-M…
Pythagoras Theorem in Noncommutative Geometry
Francesco D'Andrea
After a review of the results in arXiv:1203.3184 [math-ph] about Pythagorean inequalities for products of spectral triples, I will present some new results and discuss classes of s…
The Standard Model in Noncommutative Geometry and Morita equivalence
Francesco D'Andrea, Ludwik Dabrowski
We discuss some properties of the spectral triple describing the internal space in the noncommutative geometry approach to the Standard Model, with $A_F=\ma…
Deformations of the Canonical Commutation Relations and Metric Structures
Francesco D'andrea, Fedele Lizzi, Pierre Martinetti
Using Connes distance formula in noncommutative geometry, it is possible to retrieve the Euclidean distance from the canonical commutation relations of quantum mechanics. In this n…
Matrix Geometries Emergent from a Point
Francesco D'Andrea, Fedele Lizzi, Pierre Martinetti
We describe a categorical approach to finite noncommutative geometries. Objects in the category are spectral triples, rather than unitary equivalence classes as in other approaches…
Spectral geometry with a cut-off: topological and metric aspects
Francesco D'Andrea, Fedele Lizzi, Pierre Martinetti
Inspired by regularization in quantum field theory, we study topological and metric properties of spaces in which a cut-off is introduced. We work in the framework of noncommutativ…