Classical Noncommutative Electrodynamics with External Source

Abstract

In a $U(1{)}_{\star }$-noncommutative (NC) gauge field theory we extend the Seiberg-Witten (SW) map to include the (gauge-invariance-violating) external current and formulate - to the first order in the NC parameter - gauge-covariant classical field equations. We find solutions to these equations in the vacuum and in an external magnetic field, when the 4-current is a static electric charge of a finite size $a$, restricted from below by the elementary length. We impose extra boundary conditions, which we use to rule out all singularities, $1/r$ included, from the solutions. The static charge proves to be a magnetic dipole, with its magnetic moment being inversely proportional to its size $a$. The external magnetic field modifies the long-range Coulomb field and some electromagnetic form-factors. We also analyze the ambiguity in the SW map and show that at least to the order studied here it is equivalent to the ambiguity of adding a homogeneous solution to the current-conservation equation.

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• Dynamics of a Dirac Fermion in the presence of spin noncommutativity
• Nonlinear magnetic response of the magnetized vacuum to applied electric field
• Noncommutative magnetic moment of charged particles
• Magnetic response to applied electrostatic field in external magnetic field
• Nonlinear corrections in basic problems of electro- and magneto-statics in the vacuum
• Photon propagation in noncommutative QED with constant external field
• On the energy-momentum tensor in Moyal space
• Classical electrodynamics in a space with spin noncommutativity of coordinates
• Noncommutative Electrodynamics from $SO(2,3{)}_{\star }$ Model of Noncommutative Gravity
• Wong's Equations and Charged Relativistic Particles in Non-Commutative Space
• Noncommutative magnetic moment, fundamental length and lepton size
• When electric charge becomes also magnetic
• Noncommutative black hole in the Finslerian spacetime
• Poisson electrodynamics on $\kappa$-Minkowski space-time
• Noncommutative $SO(2,3{)}_{\star }$ Gauge Theory of Gravity
• Radiation Reaction in Non-commutative Electrodynamics