1. K. Nakagawa: in preparation.
2. L. Leplae, R. N. Sen andH. Umezawa:Progr. Theor. Phys. Suppl., Extra Number (Commemoration Issue for the 30th Anniversary of the Meson Theory by Dr.H. Yukawa), 637 (1965). The physical fields correspond to the asymptotic fields in the ordinary formulation of quantum field theory. We include the physical fields of composite particles. The physical fields are local in the sense that they satisfy the local canonical commutation relations. Though both physical fields and the basic fields are local, the coefficients of the dynamical map are nonlocal, reflecting the structure of physical particles. For example, the experimental evidence on nucleon structure does not show that the nucleon fields are nonlocal; it only shows that the coefficients in the dynamical map are nonlocal. The structure of any physical particle cannot be observed in a one-physical-particle state.
3. The effect of Coulomb-type potentials may also be interpreted as $$\dot N^\alpha \ne 0$$ , whereN α are the symmetry generators. In this case Lemma 4 in Sect.3 would no longer be valid. Significant works on this case have appeared recently:G. S. Guralnik, C. R. Hagen andT. W. B. Kibble:Phys. Rev. Lett.,13, 585 (1964);P. W. Higgs:Phys. Rev.,145, 1156 (1966). We would like to thank Prof.Dyson for discussions on this point and for calling our attention to the work byHiggs.
4. H. Umezawa:Nuovo Cimento,38, 1415 (1965);40, 450 (1965).
5. S. Kamefuchi andH. Umezawa:Nuovo Cimento,31, 429 (1964).