Field theory on $\kappa$--Minkowski space revisited: Noether charges and breaking of Lorentz symmetry

Abstract

This paper is devoted to detailed investigations of free scalar field theory on $\kappa$-Minkowski space. After reviewing necessary mathematical tools we discuss in depth the Lagrangian and solutions of field equations. We analyze the spacetime symmetries of the model and construct the conserved charges associated with translational and Lorentz symmetry. We show that the version of the theory usually studied breaks Lorentz invariance in a subtle way: There is an additional trans-Planckian mode present, and an associated conserved charge (the number of such modes) is not a Lorentz scalar.

22 pages, 1 figure, formulas in sect. III corrected

References in corpus (8)

• Fock space, quantum fields and kappa-Poincaré symmetries
• Gauge theories on the kappa-Minkowski spacetime
• From noncommutative kappa-Minkowski to Minkowski space-time
• Symplectic geometry and Noether charges for Hopf algebra space-time symmetries
• A no-pure-boost uncertainty principle from spacetime noncommutativity
• Quantum fields, non-locality and quantum group symmetries
• Quantum $\kappa$-Poincaré Algebra from de Sitter Space of Momenta
• Can we see gravitational collapse in (quantum) gravity perturbation theory?

Cited by in corpus (10)

• Fractal properties of quantum spacetime
• From noncommutative kappa-Minkowski to Minkowski space-time
• Rainbow statistics
• On kappa-deformation and triangular quasibialgebra structure
• Effective particle kinematics from Quantum Gravity
• Differential Structure on kappa-Minkowski Spacetime Realized as Module of Twisted Weyl Algebra
• Line element in quantum gravity: the examples of DSR and noncommutative geometry
• $\kappa$--Rindler space
• New twisted quantum deformations of D=4 super-Poincare algebra
• 5D Differential Calculus and Noether Analysis of Translation Symmetries in kappa-Minkowski Noncommutative Spacetime