Fwd: Re: aula

[Emanuele Tuillier Illingworth]

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MATHEMATICAL PHYSICS SECTOR SEMINARS
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Pierre Martinetti (ROMA)

Minimal length in quantum space and integrations of the line element
in Noncommutative Geometry

Abstract:
We question the emergence of a minimal length in quantum spacetime,
confronting two notions that appeared at various points in the
literature:
"quantum length" as the spectrum of an operator in the Doplicher
Fredenhagen Roberts (DFR) model on the one side; Connes "spectral
distance" in
noncommutative geometry (NCG) on the other side. Although on the
Euclidean space the two notions merge into the one of geodesic
distance, they
yield distinct results in the noncommutative framework. In particular,
on the Moyal plane, the quantum length is bounded above from zero while
the spectral distance can be arbitrarily small. We show how to
reconcile the two points of view by a natural process of "spectral
triple doubling" in NCG.
This turns the quantum length into a true distance function and,
simultaneously, emphasises the "quantum mechanics flavor" of the
spectral distance.
As an example, we apply this procedure to two classes of states: the
stationary and the coherent states of the quantum harmonic oscillator.


Thu 24 Nov, 14:00-15:00, room 137 SISSA



PAOLO ASCHIERI,
University of Piemonte Orientale, Vercelli, Italy

Deformation quantization of homomorphisms and connections.


Thu 24 Nov, 15:30-16:30, room 136 SISSA