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Electromagnetism from two matter spaces: mutual helicity and the nondegenerate completion

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abstract

We show that generic Maxwell fields can be represented within the matter-space framework by introducing two independent matter-space flows. In the one-flow formulation the electromagnetic field strength is the pull-back of a two-form on a three-dimensional matter space and therefore satisfies $F\wedge F=0$, so that a single flow captures only a degenerate, helicity-carrying sector. The minimal completion is obtained by writing $$F=G^{(1)}+G^{(2)},$$ where each sector field $G^{(I)}$ is the pull-back of a matter-space two-form from an independent flow. Each sector is individually degenerate, $G^{(I)}\wedge G^{(I)}=0$, while the full field satisfies $F\wedge F=2G^{(1)}\wedge G^{(2)}$; the invariant excluded by the one-flow theory is thus recovered as an inter-flow quantity. We interpret this structure in terms of mutual helicity: the total helicity decomposes into two self-helicity contributions and a mutual term whose exterior derivative is $F\wedge F$. Hence a configuration with vanishing mutual helicity lies in the degenerate sector, whereas a nondegenerate Maxwell field necessarily carries a nontrivial mutual helicity. A variational principle for the total field recovers the sourced Maxwell equation, the two matter-space variations combining into the full equation whenever the sector kernels intersect trivially. Generic electromagnetism is thereby reconstructed as the minimal coupled completion of two individually degenerate matter-space sectors.

years

2026 1

verdicts

UNVERDICTED 1

representative citing papers

Collective modes and screening in an electric-magnetic dual plasma

physics.plasm-ph · 2026-06-25 · unverdicted · novelty 6.0

Derives stable transverse EM branches set by electric and magnetic plasma frequencies, entrainment-induced avoided crossings in longitudinal sector with stability condition κ²<1, and a magnetically neutral branch where net magnetic current vanishes but screened response remains.

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  • Collective modes and screening in an electric-magnetic dual plasma physics.plasm-ph · 2026-06-25 · unverdicted · none · ref 14 · internal anchor

    Derives stable transverse EM branches set by electric and magnetic plasma frequencies, entrainment-induced avoided crossings in longitudinal sector with stability condition κ²<1, and a magnetically neutral branch where net magnetic current vanishes but screened response remains.