Constitutive relations and Schroedinger's formulation of nonlinear electromagnetic theories
Abstract
We present a systematic study of nonlinear and higher derivatives extensions of electromagnetism. We clarify when action functionals S[F] can be explicitly obtained from arbitrary (not necessarily self-dual) nonlinear equations of motion. We show that the "Deformed twisted self-duality condition" proposal originated in the context of supergravity counterterms is actually the general framework needed to discuss self-dual theories starting from a variational principle. We generalize to nonlinear and higher derivatives theories Schroedinger formulation of Born-Infeld theory, and for the latter, and more in general for nonlinear theories, we derive a closed form expression of the corresponding deformed twisted self-duality conditions. This implies that the hypergeometric expression entering these duality conditions and leading to Born-Infeld theory satisfies a hidden quartic equation.
Keywords
Cite
@article{arxiv.1302.4737,
title = {Constitutive relations and Schroedinger's formulation of nonlinear electromagnetic theories},
author = {Paolo Aschieri and Sergio Ferrara},
journal= {arXiv preprint arXiv:1302.4737},
year = {2015}
}
Comments
Revised version with: integrability conditions on equations of motion; equivalence between deformed twisted self-duality conditions and equations of motion from action functionals S[F] (Section 2.5); stressed universality of the quartic equation. References added. 31 pages. To appear in JHEP