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It is by now well known that the Poincare group acts on the Moyal plane with a twisted coproduct. Poincare invariant classical field theories can be formulated for this twisted coproduct. In this paper we systematically study such a twisted Poincare action in quantum theories on the Moyal plane. We develop quantum field theories invariant under the twisted action from the representations of the Poincare group, ensuring also the invariance of the S-matrix under the twisted action of the group . A significant new contribution here is the construction of the Poincare generators using quantum fields.
We show how some classical r-matrices for the D=4 Poincare algebra can be supersymmetrized by an addition of part depending on odd supercharges. These r-matrices for D=4 super-Poincare algebra can be presented as a sum of the so-called subordinated r
For every ADE Dynkin diagram, we give a realization, in terms of usual fusion algebras (graph algebras), of the algebra of quantum symmetries described by the associated Ocneanu graph. We give explicitly, in each case, the list of the corresponding twisted partition functions
We discuss the obstruction to the construction of a multiparticle field theory on a $kappa$-Minkowski noncommutative spacetime: the existence of multilocal functions which respect the deformed symmetries of the problem. This construction is only poss
In the absence of gauge fields, quantum field theories on the Groenewold-Moyal (GM) plane are invariant under a twisted action of the Poincare group if they are formulated following [1, 2, 3, 4, 5, 6]. In that formulation, such theories also have no
We revisit the question of microcausality violations in quantum field theory on noncommutative spacetime, taking $O(x)=:phistarphi:(x)$ as a sample observable. Using methods of the theory of distributions, we precisely describe the support properties