Total momentum and other Noether charges for particles interacting in a quantum spacetime

Abstract

There has been strong interest in the fate of relativistic symmetries in some quantum spacetimes, also 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. We here tackle this problem focusing on first-quantized particles described within a Hamiltonian framework and using as 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 expose a strong link between the properties of these Noether charges and the structure of the laws of interaction among particles.

arXiv comment9 pages, Latex

References in corpus (22)

• String Theory and Noncommutative Geometry
• Noncommutative Field Theory
• Potential Sensitivity of Gamma-Ray Burster Observations to Wave Dispersion in Vacuo
• The quantum structure of spacetime at the Planck scale and quantum fields
• Nonstandard optics from quantum spacetime
• Bicrossproduct structure of $\kappa$-Poincare group and non-commutative geometry
• Generalized Lorentz invariance with an invariant energy scale
• Quantum gravity corrections to neutrino propagation
• The IR/UV Connection in the Non-Commutative Gauge Theories
• The principle of relative locality
• Quantization of Point Particles in 2+1 Dimensional Gravity and Space-Time Discreteness
• Doubly-Special Relativity: First Results and Key Open Problems
• Doubly Special Relativity theories as different bases of $\kappa$--Poincaré algebra
• Falsifiable predictions from semiclassical quantum gravity
• Generalized Weyl systems and kappa-Minkowski space
• Local Field Theory ON $\kappa$-Minkowski Space, Star Products and Noncommutative Translations
• Spacetime-noncommutativity regime of Loop Quantum Gravity
• A no-pure-boost uncertainty principle from spacetime noncommutativity
• Physics of Deformed Special Relativity
• The Phase Space Structure of Multi Particle Models in 2+1 Gravity
• Twisted Hopf symmetries of canonical noncommutative spacetimes and the no-pure-boost principle
• The DSR-deformed relativistic symmetries and the relative locality of 3D quantum gravity

Cited by in corpus (1)

• Doubly Quantum Mechanics