The Maxwell Lagrangian in purely affine gravity

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dc.creatorPoplawski, Nikodem J.
dc.date2007-02-25
dc.date2008-03-01
dc.date.accessioned2026-07-07T13:01:22Z
dc.date.available2026-07-07T13:01:22Z
dc.descriptionThe purely affine Lagrangian for linear electrodynamics, that has the form of the Maxwell Lagrangian in which the metric tensor is replaced by the symmetrized Ricci tensor and the electromagnetic field tensor by the tensor of homothetic curvature, is dynamically equivalent to the Einstein-Maxwell equations in the metric-affine and metric formulation. We show that this equivalence is related to the invariance of the Maxwell Lagrangian under conformal transformations of the metric tensor. We also apply to a purely affine Lagrangian the Legendre transformation with respect to the tensor of homothetic curvature to show that the corresponding Legendre term and the new Hamiltonian density are related to the Maxwell-Palatini Lagrangian for the electromagnetic field. Therefore the purely affine picture, in addition to generating the gravitational Lagrangian that is linear in the curvature, justifies why the electromagnetic Lagrangian is quadratic in the electromagnetic field.
dc.description9 pages; published version
dc.identifierhttps://arxiv.org/abs/gr-qc/0702129
dc.identifierhttp://arxiv.org/abs/gr-qc/0702129
dc.identifierInt.J.Mod.Phys.A23:567-579,2008
dc.identifierdoi:10.1142/S0217751X08039578
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/226130
dc.subjectGeneral Relativity and Quantum Cosmology
dc.subjectMathematical Physics
dc.titleThe Maxwell Lagrangian in purely affine gravity
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