109 citations · 712 across the 45 of their papers we have counts for
4 papers · 1 filter
Towards a Monge-Kantorovich metric in noncommutative geometry
Pierre Martinetti
We investigate whether the identification between Connes' spectral distance in noncommutative geometry and the Monge-Kantorovich distance of order 1 in the theory of optimal transp…
Length and distance on a quantum space
Pierre Martinetti, Luca Tomassini
This contribution is an introduction to the metric aspect of noncommutative geometry, with emphasize on the Moyal plane. Starting by questioning "how to define a standard meter in…
Emergence of time in quantum gravity: is time necessarily flowing ?
Pierre Martinetti
We discuss the emergence of time in quantum gravity, and ask whether time is always "something that flows"'. We first recall that this is indeed the case in both relativity and qua…
On Pythagoras' theorem for products of spectral triples
Francesco D'Andrea, Pierre Martinetti
We discuss a version of Pythagoras theorem in noncommutative geometry. Usual Pythagoras theorem can be formulated in terms of Connes' distance, between pure states, in the product…