Failure of microcausality in noncommutative field theories
arXiv:0802.0997 · doi:10.1103/PhysRevD.77.125013
Abstract
We revisit the question of microcausality violations in quantum field theory on noncommutative spacetime, taking as a sample observable. Using methods of the theory of distributions, we precisely describe the support properties of the commutator [O(x),O(y)] and prove that, in the case of space-space noncommutativity, it does not vanish at spacelike separation in the noncommuting directions. However, the matrix elements of this commutator exhibit a rapid falloff along an arbitrary spacelike direction irrespective of the type of noncommutativity. We also consider the star commutator for this observable and show that it fails to vanish even at spacelike separation in the commuting directions and completely violates causality. We conclude with a brief discussion about the modified Wightman functions which are vacuum expectation values of the star products of fields at different spacetime points.
LaTeX, 22 pages; v2: minor updates to agree with published version, added reference
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Cited by in corpus (11)
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- Moyal multiplier algebras of the test function spaces of type S
- Deformations of quantum field theories on spacetimes with Killing vector fields
- Algebras with convergent star products and their representations in Hilbert spaces
- Wedge locality and asymptotic commutativity
- Propagators and Matrix Basis on Noncommutative Minkowski Space
- Deformations of half-sided modular inclusions and non-local chiral field theories
- Linear hyperbolic PDEs with non-commutative time
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- Commutative deformations of general relativity: nonlocality, causality, and dark matter
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