Classical electrodynamics on Snyder space

Abstract

A formulation of classical electrodynamics on an energy-momentum background of constant, non-zero curvature is given. The procedure consists of taking the formulation of standard electrodynamics in the energy-momentum representation, and promoting the energy-momentum vector to belong to a constant (non-zero) curvature space. In particular, special emphasis is given to the definition of integration measure and generalized Dirac's delta function. Finally, simple physical problems as plane waves (solutions outside sources) and point charges are discussed in this context, where the self-energy of a point charge is shown to be finite.

Accepted for publication in PRD

References in corpus (16)

• String Theory and Noncommutative Geometry
• Noncommutative Field Theory
• Quantum Field Theory on Noncommutative Spaces
• The quantum structure of spacetime at the Planck scale and quantum fields
• Quantum gravity and minimum length
• Lorentz invariance with an invariant energy scale
• Relativity in space-times with short-distance structure governed by an observer-independent (Planckian) length scale
• Testable scenario for Relativity with minimum-length
• Bicrossproduct structure of $\kappa$-Poincare group and non-commutative geometry
• Minimal Length Scale Scenarios for Quantum Gravity
• Generalized Lorentz invariance with an invariant energy scale
• The algebraic structure of the generalized uncertainty principle
• The principle of relative locality
• Classical and quantum mechanics of the nonrelativistic Snyder model
• Spectrum of the hydrogen atom in Snyder space in a semiclassical approximation
• Relative-locality phenomenology on Snyder spacetime

Cited by in corpus (6)

• Bumblebee gravity and particle motion in Snyder noncommutative spacetime structures
• Geometrizing the Klein-Gordon and Dirac equations in Doubly Special Relativity
• Doubly special relativity as a non-local quantum field theory
• Covariant dynamics on the momentum space
• Covariant dynamics on the energy-momentum space: scalar field theory
• Statistical physics on Euclidean Snyder space: connections with the GUP and cosmological implications