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: Proca field, charged scalar field interacting with electromagnetism and gravitation, and for few other interesting physical theories.
General Relativity is a Gauge Type Theory
FERRARIS, Marco;
1982-01-01
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: Proca field, charged scalar field interacting with electromagnetism and gravitation, and for few other interesting physical theories.
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