Field-strength formulation of gauge theories. The Hamiltonian approach in the Abelian theory

We develop a Hamiltonian approach to the field-strength or dual formation of the Abelian gauge theory in which the potential A^μ is eliminated as a dynamical variable. Our work is based on the covariant gauge x^μA_μ(x)=0 which allows a simple elimination of A^μ in terms of the field strengths F^μν. We obtain complete results for the generating functional for the Green's functions of the theory, Z=Z[→f,→g], where →f and →g are nonlocal currents coupled to →E and →B, and illustrate some unfamiliar aspects of the new formalism.