  In recent work on Einstein gravity in four dimensions using the Ashtekar
variables, non-local loop variables have played an important role in attempts
to formulate a quantum theory. The introduction of such variables is guided by
gauge invariance, and here an infinite set of loop variables is introduced for
the Hamiltonian form of the Einstein-Maxwell theory. The loops that enter the
description naturally are the (source free) electric field lines. These
variables are invariant under spatial diffeomorphisms and they also form a
closed Poisson algebra. As such they may be useful for quantization attempts
and for studying classical solutions.
