Monte Carlo simulations of random non-commutative geometries

Barrett, John W.; Glaser, Lisa

Abstract

© 2016 IOP Publishing Ltd. Random non-commutative geometries are introduced by integrating over the space of Dirac operators that form a spectral triple with a fixed algebra and Hilbert space. The cases with the simplest types of Clifford algebra are investigated using Monte Carlo simulations to compute the integrals. Various qualitatively different types of behaviour of these random Dirac operators are exhibited. Some features are explained in terms of the theory of random matrices but other phenomena remain mysterious. Some of the models with a quartic action of symmetry-breaking type display a phase transition. Close to the phase transition the spectrum of a typical Dirac operator shows manifold-like behaviour for the eigenvalues below a cut-off scale.

Citation

Barrett, J. W., & Glaser, L. (2016). Monte Carlo simulations of random non-commutative geometries. Journal of Physics A: Mathematical and Theoretical, 49(24), Article 245001. https://doi.org/10.1088/1751-8113/49/24/245001

• Journal Article Type: Article
• Acceptance Date: Mar 7, 2016
• Online Publication Date: May 11, 2016
• Publication Date: May 11, 2016
• Deposit Date: May 20, 2016
• Publicly Available Date: May 20, 2016
• Journal: Journal of Physics A: Mathematical and Theoretical
• Print ISSN: 1751-8113
• Electronic ISSN: 1751-8121
• Publisher: IOP Publishing
• Peer Reviewed: Peer Reviewed
• Volume: 49
• Issue: 24
• Article Number: 245001
• DOI: https://doi.org/10.1088/1751-8113/49/24/245001
• Keywords: General Relativity and Quantum Cosmology; High Energy Physics - Lattice; High Energy Physics - Theory
• Public URL: https://nottingham-repository.worktribe.com/output/790432
• Publisher URL: http://dx.doi.org/10.1088/1751-8113/49/24/245001
• Additional Information: This is an author-created, un-copyedited version of an article accepted for publication in the Journal of Physics A: Mathematical and Theoretical. The publisher is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at http://dx.doi.org/10.1088/1751-8113/49/24/245001.