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We study scalar field theories on Poincare invariant commutativenonassociative spacetimes. We compute the one-loop self-energy diagrams in theordinary path integral quantization scheme with Feynman's prescription, andfind that the Cutkosky rule is satisfied. This property is in contrast withthat of noncommutative field theory, since it is known that noncommutativefield theory with space/time noncommutativity violates unitarity in the abovestandard scheme, and the quantization procedure will necessarily becomecomplicated to obtain a sensible Poincare invariant noncommutative fieldtheory. We point out a peculiar feature of the non-locality in ournonassociative field theories, which may explain the property of the unitaritydistinct from noncommutative field theories. Thus commutative nonassociativefield theories seem to contain physically interesting field theories ondeformed spacetimes.Comment: 25 pages, 9 figures ; appendix and references adde

One-loop unitarity of scalar field theories on Poincaré invariant commutative nonassociative spacetimes