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arXiv · hep-th/0309216

The Non-Commutative λϕ^{4} Model

W. Bietenholz·F. Hofheinz·J. Nishimura
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Abstract

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 λϕ^{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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W. Bietenholz, F. Hofheinz, J. Nishimura. 2003-09-23. The Non-Commutative λϕ^{4} Model. https://arxiv.org/abs/hep-th/0309216

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