Quantum Corrections to Classical Nonlinear Meson Theory

Abstract

For a linear Einstein-Bose field of large amplitude it is well known that the classical approximation is quite good for treating certain problems; the validity of this conclusion for the case of a nonlinear field is investigated here. In order to compare the classical and quantized versions of a nonlinear meson theory, we consider the problem of calculating the energy of interaction of the field with a given static source distribution. The quantized theory is treated in such a way that the classical result appears as a first approximation; the quantum corrections then include infinite renormalizations of the original parameters of the theory plus finite corrections to the energy. Part of these corrections are estimated and are found to become increasingly important with increasing source strength, contrary to the usual assumption. Since only a small part of the total quantum correction can be estimated by the present methods, a complete calculation might give a value very much larger or very much smaller than that given here; nevertheless, it is possible to conclude that the nature of quantum corrections is such that they cannot be treated as small perturbations.