Total Momentum and Other Noether Charges for Particles Interacting in a Quantum Spacetime

There has been strong interest in the fate of relativistic symmetries in some quantum spacetimes, partly because of its possible relevance for high-precision experimental tests of relativistic properties. However, the main technical results obtained so far concern the description of suitably deformed relativistic symmetry transformation rules, whereas the properties of the associated Noether charges, which are crucial for the phenomenology, are still poorly understood. Here, we tackle this problem focusing on first-quantized particles described within a Hamiltonian framework and using as a toy model the so-called “spatial kappa-Minkowski noncommutative spacetime”, where all the relevant conceptual challenges are present but, as here shown, in technically manageable fashion. We derive the Noether charges, including the much-debated total momentum charges, and we reveal a strong link between the properties of these Noether charges and the structure of the laws of interaction among particles.