Tomonaga Approximation in Meson Theory
Hiroichi Hasegawa · Progress of Theoretical Physics · 1952
Recent study of the meson theory seems to have much success.Both perturbation theory including the higher order radiative corrections and strong coupling ,theory succeed to describe the nature of meson-nucleon interaction at least qualitatively and sometimes quantitatively.Inspite of the successes, we may ask whether the methods of calculations in !;,oth theories are adapted to the problem or not.It is probable that the coupling of mesons with nucleons is rather large but not so extremely, i.e. lies in the so-called" intermediate" region, Tomonaga proposed one method of appro' ximation applicable in this region, which is based on Ritz's variation principle.Moreover, he showed that the result agrees in the two limiting cases with those from the conventional theories, i.e. in the weak coupling limit with that of the usual perturbation theory and in the strong coupling limit.with that of the strong coupling theory.It may be worthy of extend• ing his theory and comparing the results with those of the conventional theories for the various types of the mesons.Here Tomonaga approximation is applied to the scalar and pseudoscalar mesons, neutral, charged and symmetrical.To solve the Schroedinger equationwe treat all the problem in Fock space.1Jf is expanded as follows: