Microcausality of Dirac field on noncommutative spacetime
Abstract
Description
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.
21 pages, Latex, v3, some mistakes corrected
21 pages, Latex, v3, some mistakes corrected