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arXiv · 2604.15745

Dirac-Bergmann analysis of SW-mapped non-commutative $U(1)$ electrodynamics with external currents

J. Manuel Cabrera·A. G. Andarcia Caballero·J. M. Paulin Fuentes
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Abstract

Non-commutative electrodynamics obtained through the Seiberg-Witten map ceases to have equivalent action-level and equation-level realizations once fixed external currents are introduced, and in the action-level construction associated with the Banerjee current map the canonical location of this source-induced obstruction has remained unclear. Working in the full phase space and treating the current as prescribed and non-dynamical, we apply the Dirac-Bergmann algorithm without imposing current conservation as an external condition. The preservation of the Gauss-type secondary constraint produces a third-stage candidate whose phase-space expression is shown to be algebraically identical, at first order in the non-commutativity parameter and for purely space-space non-commutativity, to the canonical pullback of the divergence of the mapped Euler-Lagrange equations. This identity locates the source-compatibility obstruction directly within the Dirac chain. For generic inhomogeneous sources, the next consistency step feeds this object back into the primary multiplier through a source-dependent kernel, so the chain closes by multiplier fixing rather than by the generic appearance of a quaternary constraint. Reduced-phase-space results, including the gauge generator, Dirac brackets and degree-of-freedom count, are obtained only in a restricted sufficient first-class subcase; no broader claim is made for arbitrary source profiles.

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J. Manuel Cabrera, A. G. Andarcia Caballero, J. M. Paulin Fuentes. 2026-04-20. Dirac-Bergmann analysis of SW-mapped non-commutative $U(1)$ electrodynamics with external currents. https://arxiv.org/abs/2604.15745

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