Theory of Currents,σModel, and the Spherical Top in the Internal Space

A Lagrangian field theory is constructed which gives a canonical realization of the recently proposed theory of currents. It is very similar to Gell-Mann and Levy's $\sigma$ model, but with some crucial differences. It is the second-quantized theory of the spherical top in the internal space, thus implying some connection the strong-coupling theory.