On "full" twisted Poincare' symmetry and QFT on Moyal-Weyl spaces

Abstract

We explore some general consequences of a proper, full enforcement of the "twisted Poincare'" covariance of Chaichian et al. [14], Wess [50], Koch et al. [34], Oeckl [41] 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 $\star$-tensor product in the parlance of Aschieri et al. [3,4]) prescription for any coordinates 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 Poincaré transformation properties remain undeformed. As a consequence, in QFT (even with space-time noncommutativity) one can reproduce notions (like space-like 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 QM and QFT's where the effect of space(time) noncommutativity amounts to a practically unobservable common noncommutative translation of all reference frames.

Latex file, 24 pages. Final version to appear in PRD

References in corpus (1)

• A Gravity Theory on Noncommutative Spaces

Cited by in corpus (17)

• Twisting all the way: from Classical Mechanics to Quantum Fields
• Towards Quantum Noncommutative $\kappa$-deformed Field Theory
• Spectrum of the non-commutative spherical well
• Twisted Noncommutative Field Theory with the Wick-Voros and Moyal Products
• Covariant particle statistics and intertwiners of the kappa-deformed Poincare algebra
• Braided quantum field theories and their symmetries
• Twisted Hopf symmetries of canonical noncommutative spacetimes and the no-pure-boost principle
• Noncommutativity and theta-locality
• Noncommutative fields and actions of twisted Poincare algebra
• Duality and Braiding in Twisted Quantum Field Theory
• Domain wall solitons and Hopf algebraic translational symmetries in noncommutative field theories
• Failure of microcausality in noncommutative field theories
• Summary of session A4 at the GRG18 conference: Alternative Theories of Gravity
• Wilson Loops and Area-Preserving Diffeomorphisms in Twisted Noncommutative Gauge Theory
• The Weyl-Heisenberg Group on the Noncommutative Two-Torus: A Zoo of Representations
• Noncommutative Coordinates Invariant under Rotations and Lorentz Transformations
• On the Correspondence between Poincaré Symmetry of Commutative QFT and Twisted Poincaré Symmetry of Noncommutative QFT