New representation for Lagrangians of self-dual nonlinear electrodynamics

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dc.creatorIvanov, E. A.
dc.creatorZupnik, B. M.
dc.date2002-02-28
dc.date2002-05-12
dc.date.accessioned2026-07-07T04:13:11Z
dc.date.available2026-07-07T04:13:11Z
dc.descriptionWe elaborate on a new representation of Lagrangians of 4D nonlinear electrodynamics including the Born-Infeld theory as a particular case. In this new formulation, in parallel with the standard Maxwell field strength $F_{αβ}, \bar{F}_{\dotα\dotβ}$, an auxiliary bispinor field $V_{αβ}, \bar{V}_{\dotα\dotβ}$ is introduced. The gauge field strength appears only in bilinear terms of the full Lagrangian, while the interaction Lagrangian $E$ depends on the auxiliary fields, $E = E(V^2, \bar V^2)$. The generic nonlinear Lagrangian depending on $F,\bar{F}$ emerges as a result of eliminating the auxiliary fields. Two types of self-duality inherent in the nonlinear electrodynamics models admit a simple characterization in terms of the function $E$. The continuous SO(2) duality symmetry between nonlinear equations of motion and Bianchi identities amounts to requiring $E$ to be a function of the SO(2) invariant quartic combination $V^2\bar V^2$, which explicitly solves the well-known self-duality condition for nonlinear Lagrangians. The discrete self-duality (or self-duality under Legendre transformation) amounts to a weaker condition $E(V^2, \bar{V}^2) = E(-V^2, -\bar{V}^2)$. We show how to generalize this approach to a system of $n$ Abelian gauge fields exhibiting U(n) duality. The corresponding interaction Lagrangian should be U(n) invariant function of $n$ bispinor auxiliary fields.
dc.descriptionLatex file, 11 pages, Based on the talk on the simposium "Supersymmetries and quantum symmetries", Karpacz, Poland, September 21-25, 2001; References and note added, acknowledgements are corrected
dc.identifierhttps://arxiv.org/abs/hep-th/0202203
dc.identifierhttp://arxiv.org/abs/hep-th/0202203
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/51165
dc.subjectHigh Energy Physics - Theory
dc.titleNew representation for Lagrangians of self-dual nonlinear electrodynamics
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