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Noncommutative geometry in physics

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Published 9 August 2023 • © 2023 IOP Publishing Ltd
, , Noncommutative Geometry in Physics Citation Paolo Aschieri et al 2023 J. Phys. A: Math. Theor. 56 350201 DOI 10.1088/1751-8121/acea09

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Author e-mails

andrzej.sitarz@uj.edu.pl

Author affiliations

1 Dipartimento di Scienze e Innovatione Teconologica, University of Piemonte Orientale "Amedeo Avogadro", Viale T. Michel, 15121 Alessandria, Italy

2 Università di Napoli Federico II, P.le Tecchio 80, Naples I-80126, Italy

3 Department of Physics, Yeshiva University, 245 Lexington Avenue, New York, NY 10016, United States of America

4 Uniwersytet Jagiellonski w Krakowie Wydzial Fizyki Astronomii i Informatyki Stosowanej, Łojasiewicza 11, Krakow 30-348, Poland

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5 Author to whom any correspondence should be addressed.

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Dates

  1. Received 20 July 2023
  2. Accepted 24 July 2023
  3. Published

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Method: Single-anonymous
Screened for originality? Yes

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Noncommutative geometry is a broad mathematical paradigm derived from various branches of mathematics (including operator algebras, differential geometry, index theory, and others) and physics (including quantum mechanics and quantum field theory). As a result, it pervades various research directions in both disciplines. Through topical reviews and research papers, the goal of this issue is to present an up-to-date account of the many aspects of the emergence of noncommutativity in theoretical and mathematical physics.

It should help the scientific community recognize how active the field is due to the wide range of research topics it addresses: quantum field theory, renormalization, string theory, topological states of matter, condensed matter, exactly solvable models in quantum statistical mechanics, elementary particle physics (Standard Model and grand unified theories), gravity, quantum cosmology, and quantum gravity phenomenology.

Moreover, we hope that this issue will have an impact on the larger physics community and help it overcome the frequent language difficulty associated with noncommutative geometry, which is due to its cross-disciplinary nature and the application of advanced mathematics from various research fields. The aim is to present physics as described in noncommutative geometry and to motivate noncommutative geometries in light of their relevance and potential applications in physics without sacrificing mathematical rigor. As a result, this volume helps to bridge the gap between the mathematics and physics communities who are interested in noncommutative geometry physics.

This issue contains six topical reviews and sixteen peer-reviewed research papers, and it was originally accompanied by a series of seminars held monthly in 2021.

We would like to thank all the authors who have contributed with their papers to this Issue, and we would also like to thank all the referees for providing constructive reviews.

The guest editors,

Paolo Aschieri

Francesco D'Andrea

Emil Prodan

Andrzej Sitarz

10.1088/1751-8121/acea09