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We extend analysis of soft charges of the four dimensional Maxwell theory and construct magnetic soft charges and the corresponding phase space. Imposing appropriate asymptotic falloff conditions, we compute the electric and magnetic soft charges and their algebra both at spatial and at null infinity. While the commutator of two electric or two magnetic soft charges vanish, the electric and magnetic soft charges satisfy infinite copies of Heisenberg algebra. We repeat the charge analysis in the electric-magnetic duality-symmetric Maxwell theory. We construct the duality-symmetric phase space in which the electric and magnetic soft charges generate the respective boundary gauge transformations. We define the duality-generating charge as the Noether charge associated with this duality and show this charge and the electric and magnetic soft charges form infinite copies of iso(2) algebra. Moreover, we study the algebra of charges associated with the global Poincare symmetry of the background Minkowski spacetime, the duality generating charge and the soft charges. We discuss physical meaning and implication of our charges and their algebra.
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