The Non-Commutative λφ^{4} Model

Details The Non-Commutative λφ^{4} Model The Non-Commutative λφ^{4} Model

2003-09-23

arxiv.org/abs/hep-th/0309216v1

Acta Phys.Polon. B34 (2003) 4711-4726

Physics

High Energy Physics

High Energy Physics - Theory

16 pages, 8 figures, talk presented at Workshop on Random Geometry, Krakow, 2003

Scientific paper

In the recent years, field theory on non-commutative (NC) spaces has attracted a lot of attention. Most literature on this subject deals with perturbation theory, although the latter runs into grave problems beyond one loop. Here we present results from a fully non-perturbative approach. In particular, we performed numerical simulations of the \lambda \phi^{4} model with two NC spatial coordinates, and a commutative Euclidean time. This theory is lattice discretized and then mapped onto a matrix model. The simulation results reveal a phase diagram with various types of ordered phases. We discuss the suitable order parameters, as well as the spatial and temporal correlators. The dispersion relation clearly shows a trend towards the expected IR singularity. Its parameterization provides the tool to extract the continuum limit.

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