Marco Panero, “Quantum Field Theory in a Non-Commutative Space: Theoretical Predictions and Numerical Results on the Fuzzy Sphere”, SIGMA, 2006, Volume 2,081, 14 pp.

This article is cited in 37 papers

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

Marco Panero

School of Theoretical Physics, Dublin Institute for Advanced Studies, 10 Burlington Road, Dublin 4, Ireland

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.

Keywords: non-commutative geometry; matrix models; non-perturbative effects; phase transitions.

MSC: 58B34; 81R60

Received: September 29, 2006; in final form November 10, 2006; Published online November 17, 2006

Language: English

DOI: 10.3842/SIGMA.2006.081