Abstract
It is shown that the Einstein-Maxwell theory of interacting electromagnetism and gravitation, can be derived from a first-order Lagrangian, depending on the electromagnetic field and on the curvature of a symmetric affine connection Γ on the space-time M. The variation is taken with respect to the electromagnetic potential (a connection on a U(1) principal fiber bundle on M) and the ‘gravitational potential’ Γ (a connection on the GL(4, R) principal fiber bundle of frames on M). The metric tensor g does not appear in the Lagrangian, but it arises as a momentum canonically conjugated to Γ. The Lagrangians of this type are calculated also for the Proca field, for a charged scalar field interacting with electromagnetism and gravitation, and for a few other interesting physical theories.
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