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

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, g E , 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 〈 d ⃗ ̂ tot 〉 = d B ( g E 〈 J ⃗ ̂ p 〉 ℏ + g E e 〈 S ⃗ ̂ 〉 ℏ ) , with g E e = 2 d int d B , where J ⃗ ̂ p captures Stark-induced pseudoangular momentum and S ⃗ ̂ encodes any intrinsic (spin-aligned) EDM d int from symmetry-violating interactions. We define a natural electric dipole unit (the “Bohr EDM”) as d B ≡ e a 0 = 2 μ B c α ( a 0 the Bohr radius and μ B 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., | 〈 d orb 〉 | = 3 d B for the 2 s – 2 p m