Dual symmetric Lagrangian formulation of classical E-M

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DeltaV
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Joined: Mon Oct 12, 2009 5:05 am

Dual symmetric Lagrangian formulation of classical E-M

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Dual electromagnetism: helicity, spin, momentum and angular momentum
Abstract. The dual symmetry between electric and magnetic fields is an
important intrinsic property of Maxwell equations in free space. This symmetry
underlies the conservation of optical helicity and, as we show here, is closely
related to the separation of spin and orbital degrees of freedom of light (the
helicity flux coincides with the spin angular momentum). However, in the
standard field-theory formulation of electromagnetism, the field Lagrangian
is not dual symmetric. This leads to problematic dual-asymmetric forms of
the canonical energy–momentum, spin and orbital angular-momentum tensors.
Moreover, we show that the components of these tensors conflict with the
helicity and energy conservation laws. To resolve this discrepancy between the
symmetries of the Lagrangian and Maxwell equations, we put forward a dualsymmetric
Lagrangian formulation of classical electromagnetism. This dual
electromagnetism preserves the form of Maxwell equations, yields meaningful
canonical energy–momentum and angular-momentum tensors, and ensures a
self-consistent separation of the spin and orbital degrees of freedom. This
provides a rigorous derivation of the results suggested in other recent approaches.

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