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arXiv · 1106.0639

Classical Noncommutative Electrodynamics with External Source

T. C. Adorno·D. M. Gitman·A. E. Shabad·D. V. Vassilevich
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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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T. C. Adorno, D. M. Gitman, A. E. Shabad, D. V. Vassilevich. 2011-09-05. Classical Noncommutative Electrodynamics with External Source. https://doi.org/10.1103/physrevd.84.065003

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