Lorentz invariant field theory on kappa-Minkowski space

Abstract

It is by now well established that the momentum space dual to the non-commutative $\kappa$-Minkowski space is a submanifold of de Sitter space. It has been noticed recently that field theories built on such momentum space suffer from a subtle form of Lorentz symmetry breaking. Namely, for any negative energy mode the allowed range of rapidities is bounded above. In this paper we construct a complex scalar field theory with a modified action of Lorentz generators which avoids this problem. For such theory we derive conserved charges corresponding to translational and U(1) symmetries. We also discuss in some details the inner product and Hilbert space structure of the $\kappa$-deformed complex quantum field.

10 pages, no figures

References in corpus (8)

• Fock space, quantum fields and kappa-Poincaré symmetries
• Field theory on $\kappa$--Minkowski space revisited: Noether charges and breaking of Lorentz symmetry
• From noncommutative kappa-Minkowski to Minkowski space-time
• Symplectic geometry and Noether charges for Hopf algebra space-time symmetries
• Rainbow statistics
• Quantum fields, non-locality and quantum group symmetries
• Doubly Special Relativity: facts and prospects
• First results of the Noether theorem for Hopf-algebra spacetime symmetries

Cited by in corpus (31)

• Minimal Length Scale Scenarios for Quantum Gravity
• Fractional and noncommutative spacetimes
• Scalar field theory on kappa-Minkowski spacetime and translation and Lorentz invariance
• On the $\kappa$-Dirac Oscillator revisited
• Anatomy of a deformed symmetry: field quantization on curved momentum space
• Living in Curved Momentum Space
• Localization and Reference Frames in $\kappa$-Minkowski Spacetime
• Pauli-Jordan Function and Scalar Field Quantization in $\kappa$-Minkowski Noncommutative Spacetime
• Planck-scale phenomenology with anti-de Sitter momentum space
• $\kappa$-deformed complex fields and discrete symmetries
• Deformed discrete symmetries
• The Momentum Spaces of $\kappa$-Minkowski noncommutative spacetime
• The 2D $\kappa$-Dirac oscillator
• Kinematics of a relativistic particle with de Sitter momentum space
• Interplay between spacetime curvature, speed of light and quantum deformations of relativistic symmetries
• A bound on Planck-scale deformations of CPT from muon lifetime
• $\kappa$-Poincaré-comodules, Braided Tensor Products and Noncommutative Quantum Field Theory
• Signal propagation on $\kappa$-Minkowski spacetime and non-local two-point functions
• $\kappa$-Minkowski star product in any dimension from symplectic realization
• Quantum kappa-deformed differential geometry and field theory
• A group theoretic description of the $\kappa$-Poincaré Hopf algebra
• A short introduction to $\kappa$-deformation
• Quantum particles in non-commutative space-time: an identity crisis
• Lie-Poisson gauge theories and $\kappa$-Minkowski electrodynamics
• Particle-antiparticle asymmetry in a relativistic deformed kinematics
• Multiparticle states in braided lightlike $\kappa$-Minkowski noncommutative QFT
• Deformed phase spaces with group valued momenta
• Finite entanglement entropy and spectral dimension in quantum gravity
• The Weyl-Mellin quantization map for $\kappa$-Minkowski Noncommutative Spacetime
• Parity at the Planck scale
• Asymmetry in momentum space: restoring $\mathcal{C}\mathcal{P}\mathcal{T}$ invariance of $\kappa$-field theory