κ -Poincaré comodules, braided tensor products, and noncommutative quantum field theory

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.