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Microcausality of Dirac field on noncommutative spacetime

Zheng Ze Ma
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Abstract

We study the microcausality of free Dirac field on noncommutative spacetime. We calculate the vacuum and non-vacuum state expectation values for the Moyal commutator $[\barψ_α(x)\starψ_β(x),\barψ_ σ(x^{\prime})\starψ_τ(x^{\prime})]_{\star}$ of Dirac field on noncommutative spacetime. We find that they do not vanish for some cases of the indexes for an arbitrary spacelike interval, no matter whether $θ^{0i}=0$ or $θ^{0i}\neq0$. However for the physical observable quantities of Dirac field such as the Lorentz scalar $:\barψ(x)\starψ(x):$ and the current $j^μ(x)=:\barψ(x)γ^μ\starψ(x):$ etc., we find that they still satisfy the microcausality. Therefore microcausality is satisfied for Dirac field on noncommutative spacetime.

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Zheng Ze Ma. 2006-05-08. Microcausality of Dirac field on noncommutative spacetime. https://arxiv.org/abs/hep-th/0603181

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