Electrodynamics on $\kappa$-Minkowski space-time

Abstract

In this paper, we derive Lorentz force and Maxwell's equations on kappa-Minkowski space-time up to the first order in the deformation parameter. This is done by elevating the principle of minimal coupling to non-commutative space-time. We also show the equivalence of minimal coupling prescription and Feynman's approach. It is shown that the motion in kappa space-time can be interpreted as motion in a background gravitational field, which is induced by this non-commutativity. In the static limit, the effect of kappa deformation is to scale the electric charge. We also show that the laws of electrodynamics depend on the mass of the charged particle, in kappa space-time.

16 pages,minor changes, paragraph added on page 13, two new references added, to appear in Phys.Rev. D

References in corpus (16)

• Kappa-Minkowski space-time and the star product realizations
• New realizations of Lie algebra kappa-deformed Euclidean space
• Twisted Statistics in kappa-Minkowski Spacetime
• Deformed Special Relativity and Deformed Symmetries in a Canonical Framework
• Covariant realizations of kappa-deformed space
• Deformed Oscillator Algebras and QFT in $\kappa$-Minkowski Spacetime
• Gauge theories on the kappa-Minkowski spacetime
• Constraints on the quantum gravity scale from kappa - Minkowski spacetime
• Scalar field theory on kappa-Minkowski spacetime and translation and Lorentz invariance
• Newton's Equation on the kappa space-time and the Kepler problem
• $\kappa$-deformed Dirac Equation
• Maxwell's equations on the $\kappa$-Minkowski spacetime and Electric-Magnetic duality
• Low-energy constraints on kappa-Minkowski extension of the Standard Model
• Feynman problem in the noncommutative case
• From Feynman Proof of Maxwell Equations to Noncommutative Quantum Mechanics
• A Variational Formulation of Symplectic Noncommutative Mechanics

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• Generalized Poincare algebras, Hopf algebras and kappa-Minkowski spacetime
• On the $\kappa$-Dirac Oscillator revisited
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• Kappa-Minkowski spacetime, Kappa-Poincaré Hopf algebra and realizations
• $\kappa$-Poincaré invariant quantum field theories with KMS weight
• K-Poincare-Hopf algebra and Hopf algebroid structure of phase space from twist
• Twists, realizations and Hopf algebroid structure of kappa-deformed phase space
• Effects of Noncommutativity on the Black Hole Entropy
• Differential algebras on kappa-Minkowski space and action of the Lorentz algebra
• $\kappa$-Deformed Phase Space, Hopf Algebroid and Twisting
• Quantum mechanics with coordinate dependent noncommutativity
• Uniformly accelerating observer in $\kappa$-deformed space-time
• Lagrangian Formulation of a Magnetostatic Field in the Presence of a Minimal Length Scale Based on the Kempf Algebra
• The 2D $\kappa$-Dirac oscillator
• Geometrizing the Klein-Gordon and Dirac equations in Doubly Special Relativity
• Poisson gauge theory
• Minimal and maximal lengths from position-dependent noncommutativity
• Universal $\kappa$-Poincaré covariant differential calculus over $\kappa$-Minkowski space
• Differential forms and k-Minkowski spacetime from extended twist
• Hawking radiation in the kappa-spacetime
• Uniformly accelerated detector in the $\kappa$-deformed Dirac vacuum
• Hermitian realizations of kappa-Minkowski spacetime
• Implication of geodesic equation in Generalized Uncertainty Principle framework
• Twisted BRST symmetry in gauge theories on $\kappa$-Minkowski
• Vacuum energy and the cosmological constant problem in $\kappa$-Poincaré invariant field theories
• Lie-Poisson gauge theories and $\kappa$-Minkowski electrodynamics
• 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
• Directly from $H$-flux to the family of three nonlocal $R$-flux theories
• Maxwell's equations in the context of the Fock transformation and the magnetic monopole
• Maximal acceleration in non-commutative space-time and its implications
• Superdense star in a space-time with minimal length
• Exact form of Maxwell's equations and Dirac's magnetic monopole in Fock's nonlinear relativity
• Doubly special relativity as a non-local quantum field theory
• Two-particle system in Coulomb potential for twist-deformed space-time
• Poisson electrodynamics on $\kappa$-Minkowski space-time
• How does Casimir energy fall in $\kappa$-deformed space-time?
• Transition Rate and the Photoelectric Effect in the Presence of a Minimal Length
• Thermal effects of a photon gas with a deformed Heisenberg algebra
• Quantisation of $\kappa$-deformed Dirac equation
• Non-commutative correction of ideal gas thermodynamics
• Exact form of the generalized Lorentz force in Fock's nonlinear relativity
• Maxwell's equations and Lorentz force in doubly special relativity
• Fradkin-Bacry-Ruegg-Souriau vector in kappa-deformed space-time