$\kappa$-deformed Dirac Equation

Abstract

We construct a Dirac equation in $\kappa$-Minkowski spacetime and analyse its implications. This $\kappa$-deformed Dirac equation is expanded as a power series involving derivatives with respect to commutative coordinates and the deformation parameter, $a$. We show that the $\kappa$-deformation breaks the charge conjugation invariance but preserves parity and time reversal. We then study how the Hydrogen atom spectrum is modified due to the $\kappa$-deformation, applying perturbation theory. Using this, we obtain bounds on the deformation parameter $a$, which are few orders higher than the Planck length. We also show that the effects of deformation on the spectrum are distinct from that of Moyal deformation and generalized uncertainty principle.

9 pages, title changed, paper revised and bound modified, one author added

References in corpus (22)

• Universality of Quantum Gravity Corrections
• A Gravity Theory on Noncommutative Spaces
• Symmetry, Gravity and Noncommutativity
• Kappa-Minkowski space-time and the star product realizations
• New realizations of Lie algebra kappa-deformed Euclidean space
• Twisted Statistics in kappa-Minkowski Spacetime
• Noncommutative Gravity
• Deformed Oscillator Algebras and QFT in $\kappa$-Minkowski Spacetime
• Gauge theories on the kappa-Minkowski spacetime
• Towards Quantum Noncommutative $\kappa$-deformed Field Theory
• From noncommutative kappa-Minkowski to Minkowski space-time
• Covariant particle statistics and intertwiners of the kappa-deformed Poincare algebra
• Twist and Spin-Statistics Relation in Noncommutative Quantum Field Theory
• Newton's Equation on the kappa space-time and the Kepler problem
• Noncommutative Two Dimensional Gravities
• On kappa-deformation and triangular quasibialgebra structure
• Twisted Poincare Invariance, Noncommutative Gauge Theories and UV-IR Mixing
• Berry Phase Effects in the dynamics of Dirac Electrons in Doubly Special Relativity Framework
• Low-energy constraints on kappa-Minkowski extension of the Standard Model
• Z^0 \to 2γand the Twisted Coproduct of the Poincaré Group
• 'Schwinger Model' on the Fuzzy Sphere
• Index Theorem for the $q$-Deformed Fuzzy Sphere

Cited by in corpus (21)

• Electrodynamics on $\kappa$-Minkowski space-time
• Effects of quantum deformation on the spin-1/2 Aharonov-Bohm problem
• Geodesic equation in $k$-Minkowski spacetime
• Twists, realizations and Hopf algebroid structure of kappa-deformed phase space
• Uniformly accelerating observer in $\kappa$-deformed space-time
• Entanglement dynamics in $\kappa$-deformed spacetime
• Effects of quantum deformation on the integer quantum Hall effect
• Uniformly accelerated detector in the $\kappa$-deformed Dirac vacuum
• Perturbation of the ns energy levels of the hydrogen atom in rotationally invariant noncommutative space
• Time-space noncommutativity and Casimir effect
• Quantisation of Klein-Gordon field in $\kappa$ space-time: deformed oscillators and Unruh effect
• MICZ Kepler Systems in Noncommutative Space and Duality of Force Laws
• Kappa-deformed Dirac oscillator in an external magnetic field
• Photonic realization of the kappa-deformed Dirac equation
• Maximal acceleration in non-commutative space-time and its implications
• Twisted Fermionic Oscillator Algebra in $\kappa$-Minkowski space-time
• Non-Commutative space-time and Hausdorff dimension
• Propagation of spinors on a noncommutative spacetime: equivalence of the formal and the effective approach
• How does Casimir energy fall in $\kappa$-deformed space-time?
• Quantisation of Lorentz invariant scalar field theory in non-commutative space-time and its consequence
• Quantisation of $\kappa$-deformed Dirac equation