Russo, J. G. (Jorge Guillermo)Townsend, Paul K.2025-06-022025-06-0220241126-6708https://hdl.handle.net/2445/221320For any causal nonlinear electrodynamics theory that is “self-dual” (electromagnetic U(1)-duality invariant), the Legendre-dual pair of Lagrangian and Hamiltonian densities {L, H} are constructed from functions {ℓ, h} on R + related to a particle-mechanics Lagrangian and Hamiltonian. We show how a ‘duality’ relating ℓ to h implies that L and H are related by a simple map between appropriate pairs of variables. We also discuss Born’s “Legendre self-duality” and implications of a new “Φ-parity” duality. Our results are illustrated with many examples. 41 p.application/pdfengcc-by (c) Russo, J.G. et al., 2024http://creativecommons.org/licenses/by/4.0/ElectrodinàmicaCamps de galga (Física)ElectrodynamicsGauge fields (Physics)info:eu-repo/semantics/article7571122025-06-02info:eu-repo/semantics/openAccess