Theory of Currents and the Nonstrong Interactions

General perturbations around Sugawara's theory of currents are considered. The usual forms for the semistrong, electromagnetic, and weak interactions are easily incorporated, and, using a modified interaction picture, a covariant Feynman-graphical approach to the perturbation is achieved. There is some degree of uniqueness in the allowed perturbation: If infinite polynomials are to be avoided in the theory, the perturbations must be of the form $V_{\mu }{V}^{\mu }$, or $V_{\mu }{C}^{\mu }$ ($C^{\mu }$ is a canonical vector field), or $\sigma$ (the scalar density due to Bardakci, Frishman, and Halpern).