Dual Magnetic and Electric Dipole Symmetry: Pseudo Angular Momentum in Parity Space and the Electric Landé $g$-Factor

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-analogue 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 factor 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 $⟨{\hat{\vec{d}}}_{\mathrm{tot}}⟩=d_B(g_E\frac{⟨{\hat{\vec{J}}}_p⟩}{\hslash }+g_E^e\frac{⟨\hat{\vec{S}}⟩}{\hslash })$, with $g_E^e=\frac{2d_{\mathrm{int}}}{d_B}$, where ${\hat{\vec{J}}}_p$ captures Stark-induced pseudo-angular momentum and $\hat{\vec{S}}$ encodes any intrinsic (spin-aligned) EDM $d_{\mathrm{int}}$ from symmetry-violating interactions. We define a natural electric dipole unit (the ``Bohr EDM'') as $d_B\equiv e{a}_0=\frac{2{\mu }_B}{c\alpha }$ ($a_0$ the Bohr radius and ${\mu }_B$ 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.\ $|⟨d_{\mathrm{orb}}⟩|=3d_B$ for the $2s$--$2p_{m=0}$ mixing).

Accepted version of the paper

References in corpus (5)

• The electronic properties of graphene
• Many-Body Physics with Ultracold Gases
• Measurement of the permanent electric dipole moment of the neutron
• A new bound on the electron's electric dipole moment
• Active Electric Dipole Energy Sources: Transduction via Electric Scalar and Vector Potentials