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arXiv · 2407.02577

Dualities of Self-Dual Nonlinear Electrodynamics

Jorge G. Russo·Paul K. Townsend
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Abstract

For any causal nonlinear electrodynamics theory that is "self-dual" (electromagnetic $U(1)$-duality invariant), the Legendre-dual pair of Lagrangian and Hamiltonian densities $\{\mathcal{L},\mathcal{H}\}$ are constructed from functions $\{\ell,h\}$ on ${\bf R}^+$ related to a particle-mechanics Lagrangian and Hamiltonian. We show how a `duality' relating $\ell$ to $h$ implies that $\mathcal{L}$ and $\mathcal{H}$ 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.

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Jorge G. Russo, Paul K. Townsend. 2024-09-16. Dualities of Self-Dual Nonlinear Electrodynamics. https://arxiv.org/abs/2407.02577

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