We discuss the obstruction to the construction of a multiparticle field theory on a κ -Minkowski noncommutative spacetime: the existence of multilocal functions which respect the deformed symmetries of the problem. This construction is only possible for a lightlike version of the commutation relations, if one requires invariance of the tensor product algebra under the coaction of the κ -Poincaré group. This necessitates a braided tensor product. We study the representations of this product, and prove that κ -Poincaré-invariant N -point functions belong to an Abelian subalgebra, and are therefore commutative. We use this construction to define the 2-point Whightman and Pauli–Jordan functions, which turn out to be identical to the undeformed ones. We finally outline how to construct a free scalar κ -Poincaré-invariant quantum field theory, and identify some open problems.
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