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Dual magnetic and electric dipole symmetry: Pseudoangular momentum in parity space and the electric Landé g factor

Michael E. Tobar*

  • *Contact author: michael.tobar@uwa.edu.au
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APS Open Sci. 1, 000057 – Published 7 July, 2026

DOI: https://doi.org/10.1103/xhk9-qt61

Abstract

Electric dipole moments (EDMs) are sensitive probes of fundamental symmetries and central to searches for physics beyond the standard model. We present a symmetry-based, Zeeman-analog operator framework that places magnetic and electric dipole physics on parallel footing under electromagnetic duality and introduce a polar-sector pseudo-angular-momentum degree of freedom in parity space together with an associated electric Landé g factor, gE, that organizes induced orbital dipoles. Following Ohanian's effective-current formulation of the Zeeman effect, we construct its electric dual: The wavefunction's microscopic polarization admits an equivalent effective magnetic probability-current representation, providing a field-equivalence description of parity-mixed charge displacement. In this notation, the total EDM expectation takes the unified form 〈d⃗̂tot〉=dB(gE〈J⃗̂p〉ℏ+gEe〈S⃗̂〉ℏ), with gEe=2dintdB, where J⃗̂p captures Stark-induced pseudoangular momentum and S⃗̂ encodes any intrinsic (spin-aligned) EDM dint from symmetry-violating interactions. We define a natural electric dipole unit (the “Bohr EDM”) as dB≡ea0=2μBcα (a0 the Bohr radius and μB the Bohr magneton). As a canonical analytic benchmark, we show in the hydrogenic problem that a static electric field couples within a fixed n manifold through the scaled Runge-Lenz structure, yielding a compact Landé-like description and reproducing the Stark doublet (e.g., |〈dorb〉|=3dB for the 2s–2pm=0 mixing).

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APS Open Sci. 1, 000057– Published 7 July, 2026
Vol. 1
  • Received 11 November 2025
  • Revised 21 May 2026
  • Accepted 26 June 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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