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Considerations regarding the duality rotation. Levman, Garry

Abstract

Maxwel l's equations for the vacuum are invariant under the duality rotation; however, the significance of this invariance is not well understood. The purpose of this thesis is to consider the duality rotation in greater detail than has been done previously. The duality invariance of Maxwell's equations is discussed, and it is shown that the only duality invariants bilinear in the electric and magnetic fields are arbitrary linear combinations of the components of the stress-energy-momentum tensor. It is also shown that the most general linear field transformation which leaves Maxwell's vacuum equations invariant is the duality rotation. The usual Lagrangian density for the electromagnetic field does not exhibit duality invariance. It is shown, however, that if one takes the components of the electromagnetic field tensor as field variables, then the most general Lorentz invariant Lagrangian density bilinear in the electomagnetic fields and their first derivatives is determined uniquely by the requirement of duality invariance. The ensuing field equations are identical with the iterated Maxwell equations. It is further shown that in neutrino theory the Pauli transformation of the second kind corresponds to the duality rotation.

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