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In recent work on Einstein gravity in four dimensions using the Ashtekarvariables, non-local loop variables have played an important role in attemptsto formulate a quantum theory. The introduction of such variables is guided bygauge invariance, and here an infinite set of loop variables is introduced forthe Hamiltonian form of the Einstein-Maxwell theory. The loops that enter thedescription naturally are the (source free) electric field lines. Thesevariables are invariant under spatial diffeomorphisms and they also form aclosed Poisson algebra. As such they may be useful for quantization attemptsand for studying classical solutions.Comment: 8 pages, Alberta-Thy-30-93 (RevTeX

Faraday lines and observables for the Einstein-Maxwell theory