Dual electromagnetism: helicity, spin, momentum and angular momentum

Abstract

The dual symmetry between electric and magnetic fields is an important\nintrinsic property of Maxwell equations in free space. This symmetry underlies\nthe conservation of optical helicity, and, as we show here, is closely related\nto the separation of spin and orbital degrees of freedom of light (the helicity\nflux coincides with the spin angular momentum). However, in the standard\nfield-theory formulation of electromagnetism, the field Lagrangian is not dual\nsymmetric. This leads to problematic dual-asymmetric forms of the canonical\nenergy-momentum, spin, and orbital angular momentum tensors. Moreover, we show\nthat the components of these tensors conflict with the helicity and energy\nconservation laws. To resolve this discrepancy between the symmetries of the\nLagrangian and Maxwell equations, we put forward a dual-symmetric Lagrangian\nformulation of classical electromagnetism. This dual electromagnetism preserves\nthe form of Maxwell equations, yields meaningful canonical energy-momentum and\nangular momentum tensors, and ensures a self-consistent separation of the spin\nand orbital degrees of freedom. This provides rigorous derivation of results\nsuggested in other recent approaches. We make the Noether analysis of the dual\nsymmetry and all the Poincar\\'e symmetries, examine both local and integral\nconserved quantities, and show that only the dual electromagnetism naturally\nproduces a complete self-consistent set of conservation laws. We also discuss\nthe observability of physical quantities distinguishing the standard and dual\ntheories, as well as relations to quantum weak measurements and various optical\nexperiments.\n