Quantum Field Theory in a Non-Commutative Space: Theoretical Predictions and Numerical Results on the Fuzzy Sphere

Panero, Marco (2006) Quantum Field Theory in a Non-Commutative Space: Theoretical Predictions and Numerical Results on the Fuzzy Sphere. Symmetry, Integrability and Geometry: Methods and Applications. ISSN 1815-0659

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Abstract

We review some recent progress in quantum field theory in non-commutative space, focusing onto the fuzzy sphere as a non-perturbative regularisation scheme. We first introduce the basic formalism, and discuss the limits corresponding to different commutative or non-commutative spaces. We present some of the theories which have been investigated in this framework, with a particular attention to the scalar model. Then we comment on the results recently obtained from Monte Carlo simulations, and show a preview of new numerical data, which are consistent with the expected transition between two phases characterised by the topology of the support of a matrix eigenvalue distribution.

Item Type:	Article
Uncontrolled Keywords:	non-commutative geometry, matrix models, non-perturbative effects, phase transitions
Divisions:	School of Theoretical Physics > Preprints
Date Deposited:	05 Oct 2017 19:31
Last Modified:	17 Dec 2022 10:09
URI:	https://dair.dias.ie/id/eprint/178

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