Michele Arzano

Utrecht University (Utrecht , Netherlands)

Quantum fields on curved momentum space

Abstract:
Relativistic particles with momentum space described by a group manifold provide a very interesting link between (quantum) gravity, quantum group symmetries and non-commutative field theories. In 4d the only known example of momenta living on a group is encountered in the context of the k-Poincare' algebra introduced by Lukierski et al. twenty years ago. I will discuss the construction of a one-particle Hilbert space from the classical k-deformed phase space and show how the group manifold structure of momentum space leads to an ambiguity in the quantization procedure reminiscent of the ambiguities found when quantizing fields in curved space-times. The tools introduced in the discussion of field quantization lead to a natural definition of deformed two-point function. Moving to the multiparticle sector I will discuss how the quantum group symmetry of the Hilbert space induces additional structure which reflects in a non-trivial, momentum-dependent statistics. The richer structure of the deformed Fock space allows for the possibility of entanglement between the field modes and "planckian" degrees of freedom.