Vanishing of Renormalized Charges in Field Theories with Point Interaction

A short survey of the results obtained by applying the theory of Landau, Abrikosov, and Khalatnikov to pseudoscalar meson theory is presented. An independent deduction of the explicit expressions for the Green's functions and vertex part is obtained on the basis of simple renormalizability considerations. The relation thus obtained between ${g_0}^2$, ${g_c}^2$ and the momentum cutoff $\Lambda$ is such that the theory inevitably leads to the result that for point interaction (i.e., in the limit $\Lambda \to \infty$) the renormalized charge $g_c$ must equal zero.