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It is shown that the one-loop two-point amplitude in Lorentz-invariant non-commutative (NC) 3 theory is finite after subtraction in the commutative limit and satisfies the usual cutting rule. This eliminates the unitarity problem in Lorentz-non-invariant NC field theory in the approximation considered. * ) This never means that the unitarity sum leads to a non-trivial result also in this case.
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Morita et al. (2003) studied this question.
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