ON THE EMERGENCE OF NON LOCALITY FOR QUANTUM FIELDS ENJOYING κ-POINCARE´ SYMMETRIES

A novel perspective developed in [arXiv:0710.1083] by M. Arzano underlies the deep relation between quan- tum groups and Planck-scale-suppressed non locality (determined by dynamical quantum gravity) in quantum field theory. Far from locality, symmetries of the theory cannot be described in terms of Lie algebras but need a new language, provided by non co-commutative Hopf algebras or quantum groups . This kind of quantized symmetries, acting on non commutative space-times, emerges in the low-energy limit of certain quantum gravity models. Within this perspective, we give here an insight to the issue of physically characterizing space-time symmetries of quantum groups -type and investigating quantum fields enjoying them. We focus on κ-Minkowski non commutative space-time and discuss how symmetries can be described by the κ-Poincare Hopf algebra. We then show how working on the symplectic structure of classical κ-fields suggests a new approach to the canonical quantization of mass-less free fields and present results obtained in [arXiv:0707.1329] via deformed Fock space construction. Based on preliminary work with G. Amelino-Camelia and M. Arzano, we discuss some general expectations concerning the structure of multi-particle states in the quantum-gravity realm, introducing the first elements of a toy model based on the κ-deformed bosonic symmetrization of Fock space here summarized.