(Received May 28, 1955)
The bound meson problem is studied in the p-representation of meson oscillators. (p is canonical momentum). The notion of this paper may be applied to other problems than the symmetrical scalar one. The domain of p is divided into the inner and outer regions. It is proved by application of canonical transformations that such a process is natural. In the inner region the procession of the τ-spin is dominant, which takes place as bound mesons are virtually emitted or absorbed. On the other hand, in the outer region the coupling between the radial mode of meson with the τ-spin is primarily important. Since all relevant quantities appear as functions of V|p| (V is coupling constant), we can speak about the characteristics of regions independently of V, if we choose 1/V as the unit of length of p. Then in this scale, we see that the wave functions of low-lying states are damped when the magnitude of |p| is larger than V. By way of these considerations, we can understand the characteristics of the problem over all ranges of V in a unified fashion. In a weak coupling case, the inner region is the only one to be taken into account, while the most noticeable features of a strong coupling case came from the outer region, to which the major part of a wave function belongs in this case. It is noticeable that the inner region is, however, essential to give finer details of a strong coupling case, which are of higher order in 1/V2.
With these qualitative prospects in mind, a new approach is tried to improve the results worked out by Sawada. However, our ability to treat a complicated form of operators is at present so limited that our results are not yet satisfactory. It is discussed what may be the key to the future improvement.
URL : http://ptp.ipap.jp/link?PTP/14/243/
DOI : 10.1143/PTP.14.243