Geometrizing the Klein-Gordon and Dirac equations in Doubly Special Relativity

Abstract

In this work we discuss the deformed relativistic wave equations, namely the Klein--Gordon and Dirac equations in a Doubly Special Relativity scenario. We employ what we call a geometric approach, based on the geometry of a curved momentum space, which should be seen as complementary to the more spread algebraic one. In this frame we are able to rederive well-known algebraic expressions, as well as to treat yet unresolved issues, to wit, the explicit relation between both equations, the discrete symmetries for Dirac particles, the fate of covariance, and the formal definition of a Hilbert space for the Klein--Gordon case.

18 pages

References in corpus (25)

• Planck-scale modified dispersion relations and Finsler geometry
• Riemann-Finsler geometry and Lorentz-violating kinematics
• Deformed Oscillator Algebras and QFT in $\kappa$-Minkowski Spacetime
• Field theory on $\kappa$--Minkowski space revisited: Noether charges and breaking of Lorentz symmetry
• Realization of DSR-relativistic symmetries in Finsler geometries
• Scalar field theory on kappa-Minkowski spacetime and translation and Lorentz invariance
• Scalar field theory in Snyder space-time: alternatives
• Discrete Gravity Models and Loop Quantum Gravity: a Short Review
• Anatomy of a deformed symmetry: field quantization on curved momentum space
• Analogue spacetime based on 2-component Bose-Einstein condensates
• Deformed relativity symmetries and the local structure of spacetime
• Planck-scale-modified dispersion relations in homogeneous and isotropic spacetimes
• Doubly special relativity and translation invariance
• Redshift in Finsler spacetimes
• Deformed discrete symmetries
• Beyond Special Relativity at second order
• Geometric interpretation of Planck-scale-deformed co-products
• A bound on Planck-scale deformations of CPT from muon lifetime
• Curved momentum space, locality, and generalized space-time
• Geometry of multi-particle systems with a relativistic deformed kinematics and the relative locality principle
• Relativistic deformed kinematics from locality conditions in a generalized spacetime
• Classical electrodynamics on Snyder space
• Planck-scale deformation of CPT and particle lifetimes
• Particle-antiparticle asymmetry in a relativistic deformed kinematics
• Lie algebraic deformations of Minkowski space with Poincare algebra

Cited by in corpus (11)

• Quantum-spacetime effects on nonrelativistic Schrödinger evolution
• Symmetries of $\kappa$ Minkowski space-time: A possibility of exotic momentum space geometry?
• A new perspective on Doubly Special Relativity
• Momentum gauge fields from curved momentum space through Kaluza-Klein reduction
• Doubly special relativity as a non-local quantum field theory
• Propagation of spinors on a noncommutative spacetime: equivalence of the formal and the effective approach
• Non-local quantum field theory from doubly special relativity
• Covariant dynamics on the energy-momentum space: scalar field theory
• Emergent spacetime from a Berry-inspired dynamical gauge field coupled to electromagnetism
• Formal developments in curved momentum space: the quantum field theory roadmap
• Hilbert space representation for quasi-Hermitian position-deformed Heisenberg algebra and Path integral formulation