Significance of the Redundant Solutions of the Low-Wick Equation

Abstract

The content of the Low-Wick scattering formalism is studied, using the example of a class of exactly soluble meson theories with fixed-source interaction. The theories in question describe a set of harmonic oscillators with an arbitrary distribution of frequencies, coupled to a scalar meson field by means of their total dipole moment. The Low equation for scattering of a meson is shown to possess infinitely many solutions. These are compared with the exact, explicit solution of the same problem, and it is shown that there is a one-to-one correspondence between a particular choice of theory (number of oscillators and their frequencies) and a given one of the aforementioned solutions of the Low equation. A similar situation is shown to obtain for symmetric pseudoscalar theory, and it is made plausible thereby that Chew and Low have chosen the particular solution appropriate to their Hamiltonian.