Talk detail

Participant	Martinetti, Pierre
Institution	Università di Trieste - via Valerio - Trieste - Trieste - Italy

Session	QF1	Accepted		Order	Time
Talk	Oral abstract	Title	Quantum Length, Quantum Geodesics
Coauthors
Abstract	It is a common idea that a quantum spacetime is a geometrical object in which the length is quantized. This is usually interpreted as the impossibility to measure a distance below a certain quantity, usually the Planck length. Most often this minimal length is obtained as the non-zero minimum of a suitably defined length operator, as in the Doplicher, Fredenhagen, Roberts model. On the contrary, in Connes noncommutative geometry one has a notion of distance between quantum states that can be as small as desired. At first sight this seems in contradiction with the idea of minimal length. However we will show how to quantize this distance (by doubling the spectral triple of the Moyal plane), and how this is equivalent to de-quantizing the quantum length of the DFR model. This shows that Connes spectral distance and the DFR length operator captures the same metric information, at least as long as one considers coherent states. Between eigenstates of the harmonic oscillators, there remains a difference. Our conclusion is that Connes distance and the DFR length operator make a similar proposal on how to quantize the length element, but offer distinct views on the quantization of geodesics.
Pdf file

Session	QF3	Accepted		Order	Time
Talk	Oral abstract	Title	Twisted spectral triple and the standard model of elementary particles
Coauthors
Abstract	Noncommutative Geometry provides a generalization of Riemannian geometry in which the Standard Model of elementary particles is obtained as a pure gravitational theory. It gives a way to compute the mass of the Higgs boson, which is obtained as a connection 1-form living on the noncommutative part of the geometry. The recent discovery of a 126 GeV Higgs boson yielded some particle physicist to postulate the existence of another scalar field, in order to avoid some instability in the Standard Model. We will show how to generate this new field in the noncommutative geometry framework, by twisting (in the sense of Connes, Moscovici), the spectral triple of the standard model. We will generalize the construction to arbitrary spectral triples, and show how the model recently developed in collaboration with Devastato and Lizzi is one of the few possible twists of the standard model.
Pdf file