On the emergence of non locality for quantum fields enjoying κ-poincar´e symmetries

Abstract EN

A novel perspective developed in [arXiv:0710.1083] by M.

Arzano underlies the deep relation between “quantum 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-Poincar´e 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.