Toward an axiomatic formulation of noncommutative quantum field theory

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<jats:p>We propose new Wightman functions as vacuum expectation values of products of field operators in the noncommutative space–time. These Wightman functions involve the ⋆-product among the fields, compatible with the twisted Poincaré symmetry of the noncommutative quantum field theory (NC QFT). In the case of only space–space noncommutativity (θ0i = 0), we prove the CPT theorem using the noncommutative form of the Wightman functions. We also show that the spin-statistics theorem, demonstrated for the simplest case of a scalar field, holds in NC QFT within this formalism.</jats:p>

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