FARADAY LINES AND OBSERVABLES FOR THE EINSTEIN-MAXWELL THEORY

In recent work on Einstein gravity in four dimensions using the Ashtek ar variables, non-local loop variables have played an important role i n attempts to formulate a quantum theory. The introduction of such var iables is guided by gauge invariance, and here an infinite set of loop variables is introduced for the Hamiltonian form of the Einstein-Maxw ell theory. The loops that enter the description naturally are the (so urce free) electric field lines. These variables are invariant under s patial diffeomorphisms and they also form a closed Poisson algebra. As such they may be useful for quantization attempts and for studying cl assical solutions. It is further shown how to construct spatially diff eomorphism invariant wavefunctions based on loops that are parametrize d by two arbitrary functions of two variables.