Full twisted Poincaré symmetry and quantum field theory on Moyal-Weyl spaces

Abstract

We explore some general consequences of a proper, full enforcement of the 'twisted Poincare' covariance of Chaichian et al., Wess, Koch et al., and Oeckl upon many-particle quantum mechanics and field quantization on a Moyal-Weyl noncommutative space(time). This entails the associated braided tensor product with an involutive braiding (or *-tensor product in the parlance of Aschieri et al.) prescription for any coordinate pair of x, y generating two different copies of the space(time); the associated nontrivial commutation relations between them imply that x-y is central and its Poincare transformation properties remain undeformed. As a consequence, in quantum field theory (QFT) (even with space-time noncommutativity) one can reproduce notions (like spacelike separation, time- and normal-ordering, Wightman or Green's functions, etc.), impose constraints (Wightman axioms), and construct free or interacting theories which essentially coincide with the undeformed ones, since the only observable quantities involve coordinate differences. In other words, one may thus well realize quantum mechanics (QM) and QFT's where the effect of space(time) noncommutativity amounts to a practically unobservable common noncommutative translation of all reference frames.