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The Eddington Lagrangian in the purely affine formulation of generalrelativity generates the Einstein equations with the cosmological constant. TheFerraris-Kijowski purely affine Lagrangian for the electromagnetic field, whichhas the form of the Maxwell Lagrangian with the metric tensor replaced by thesymmetrized Ricci tensor, is dynamically equivalent to the Einstein-MaxwellLagrangian in the metric formulation. We show that the sum of the two affineLagrangians is dynamically inequivalent to the sum of the analogous Lagrangiansin the metric-affine/metric formulation. We also show that such a constructionis valid only for weak electromagnetic fields. Therefore the purely affineformulation that combines gravitation, electromagnetism and the cosmologicalconstant cannot be a simple sum of terms corresponding to separate fields.Consequently, this formulation of electromagnetism seems to be unphysical,unlike the purely metric and metric-affine pictures, unless the electromagneticfield couples to the cosmological constant.Comment: 14 pages, extended and combined with gr-qc/0701176; published versio

GRAVITATION, ELECTROMAGNETISM AND THE COSMOLOGICAL CONSTANT IN PURELY AFFINE GRAVITY