Failure of microcausality in quantum field theory on noncommutative spacetime

Abstract

The star commutator of $:\varphi (x)\star \varphi (x):$ with $:\varphi (y)\star \varphi (y):$ fails to vanish at equal times and thus also fails to obey microcausality at spacelike separation even for the case in which ${\theta }^{0i}=0$. The failure to obey microcausality for this sample observable implies that this form of noncommutative field theory fails to obey microcausality in general. This result also holds for general fields and observables. We discuss possible responses to this problem.

10 pages

References in corpus (3)

• On a Lorentz-Invariant Interpretation of Noncommutative Space-Time and Its Implications on Noncommutative QFT
• A Gravity Theory on Noncommutative Spaces
• New concept of relativistic invariance in NC space-time: twisted Poincaré symmetry and its implications

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