Charged-Scalar Strong-Coupling Theory

A treatment of the charged-scalar strong-coupling theory is given which employs a somewhat different choice of variables than that usually used; one which is more convenient for a discussion of the effects of quantum mechanical field fluctuations. The expansion parameter of the strong-coupling theory is shown to be $\left(\frac{1}{g^2}\right)\ln \left(\frac{1}{\mathrm{Ka}}\right)$, where $a$ is the source radius. The isobar energy is calculated to order $\frac{1}{g^4}$, and terms of order $\left(\frac{1}{g^2}\right)\ln \left(\frac{1}{\mathrm{Ka}}\right)$ relative to the leading $\frac{1}{g^2}$ term are found to appear. Similar terms occur in the charge-renormalization factor. The logarithmic term in the isobar energy is found to be precisely that required to renormalize the charge; that is, the isobar energy, if expressed in terms of the renormalized coupling constant, is explicitly independent of the source radius.