School and Conference on Modern Mathematical Physics

9 - 14 September 2019, Belgrade, Serbia


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    E-mail: mphys10@ipb.ac.rs


Anna Pachol

Digital quantum geometries

Noncommutative geometry, as the generalised notion of geometry, allows us to model the quantum gravity effects in an effective description without full knowledge of quantum gravity itself. On a curved space one must use the methods of Riemannian geometry - but in their quantum version, including quantum differentials, quantum metrics and quantum connections.

The mathematical framework behind it is the noncommutative differential graded algebra. After presenting the general framework, I will discuss some recent results on noncommutative Riemannian geometries in small dimensions, working over the field F_2 of 2 elements and with coordinate algebras up to dimension n<=3 (arXiv:1807.08492). We have found a rich moduli of examples for n=3 and top form degree 2, including 9 that are Ricci flat but not flat. The choice of the finite field in this framework proposes a new kind of 'discretisation scheme', which we called the 'digital geometry'.


Institute of Physics Belgrade (University of Belgrade)
Belgrade, Serbia
Faculty of Mathematics (University of Belgrade)
Belgrade, Serbia
Mathematical Institute (Serbian Academy of Sciences and Arts)
Belgrade, Serbia
Faculty of Science (University of Kragujevac)
Kragujevac, Serbia
Serbian Academy of Sciences and Arts (SASA)
Belgrade, Serbia


Institute of Nuclear Sciences "VinĨa" (University of Belgrade)
Belgrade, Serbia
Institute of Physics (University of Kragujevac)
Kragujevac, Serbia
Faculty of Physics (University of Belgrade)
Belgrade, Serbia
Faculty of Sciences (University of Novi Sad)
Novi Sad, Serbia
School of Electrical Engineering (University of Belgrade)
Belgrade, Serbia
SEENET-MTP (Southeastern European Network in Mathematical and Theoretical Physics)
Nis, Serbia