Noncommutativity and theta-locality

Details Noncommutativity and theta-locality Noncommutativity and theta-locality

2007-08-08

arxiv.org/abs/0708.1151v2

J.Phys.A40:14593-14604,2007

Physics

High Energy Physics

High Energy Physics - Theory

LaTeX, 17 pages, no figures; minor changes to agree with published version

Scientific paper

10.1088/1751-8113/40/48/020

In this paper, we introduce the condition of theta-locality which can be used as a substitute for microcausality in quantum field theory on noncommutative spacetime. This condition is closely related to the asymptotic commutativity which was previously used in nonlocal QFT. Heuristically, it means that the commutator of observables behaves at large spacelike separation like $\exp(-|x-y|^2/\theta)$, where $\theta$ is the noncommutativity parameter. The rigorous formulation given in the paper implies averaging fields with suitable test functions. We define a test function space which most closely corresponds to the Moyal star product and prove that this space is a topological algebra under the star product. As an example, we consider the simplest normal ordered monomial $:\phi\star\phi:$ and show that it obeys the theta-locality condition.

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