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The quantum energy of one soliton state in the periodic exponential lattice is calcu· lated by the WKB (semi-classical) approximation method. And problems to clarify the notion of the quantum theory of solitons are briefly discussed.

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1289A model for reactions of composite hadrons is presented, which intl['oduces the effect· of the motion of each urbaryon as a Dirac particle. As a consequence the non-vanishing polarization function P(O, E) is obtained even for the forward reactions which receive contributions only from a single one of the three diagrams in Fig. 2. This result is compared with that of a model which neglects the internal structure of hadrons. §I. IntroductionThe success of the non~relativistic quark model and the additivity assumption in explaining some static properties of hadrons, the possible existence of the hard core in the hadronic scattering phenomena, and the damping character of electro~ magnetic form factors of the proton, strongly suggest that a hadron is actually ·constructed of more fundamental subhadronic matter (urbaryon). Theories based on analyticity such as the Regge pole hypothesis also suggest that a hadron is a composite system in some sense.Until now, however, the urbaryon has never been observed experimentally, and further there is no theoretical basis which necessitates the urbaryon to be observed as a real particle. The simple urbaryon model must have many curious features. We believe that it is important to investigate to what extent the present :field theoretic particle picture is applicable to the urbaryon.The present :field theoretic particle picture assumes as attributes of the urbaryon, the four~momentum, mass, spin, statistics and so forth on the one hand, and the unitary spin on the other hand. The former attributes are to be closely related to the framework of the space~time in which the urbaryon does exist. Consequently, it seems important to investigate whether the urbaryon has these attributes or not, since, if so, the urbaryon would be expected to be observed experimentally as a real particle. On the other hand, the unitary spin is not directly connected with the space~time properties in the framework of the present quantum :field theory, so it seems unable to get a definite answer as to whether a hadron is actually constructed of urbaryons as an existence in a real space~time framework.

It has been pointed out by several authors that the absorptive part of KL 0~ p.+ p. -is almost saturated by the on-massshell 2r intermediate state 1 > • 2 > and if, in addition, CP-conservation holds, then the theoretical lower bound for the KL 0~p .+ p.decay rate contradicts the experimental upper bound. 8 > Christ and Lee have obtained the in-equality4> [Rate (KL 0~p .+ p.-) Jl 12 < (Re e) [Rate (Ki~P.+ p.-)]11 2 , (1) on the assumptions that (i) the absorptive part of the KL 0~2 r decay amplitude is zero, (ii) the absorptive part of the KL 0 ~p.+ p.decay amplitude is due only to the on-mass-shell 2r intermediate state and (iii) both CPT-invariance and quantum electrodynamics are valid, but CP-conservation is not, and using the experimental upper bound on the branching ratio, 5 > Rate(KL 0~p .+ p.-) /Rate(KL 0~a ll) xi.The purpose of this note is to discuss the several consequences from the inequality (1) 0 1. Contradiction with the super weak theory. When we define the CP-conserving and -nonconserving decay amplitudes as follows, T2"-= 2. On the lower bound for CP-nonconservation. The inequality (1) is rewritten using the amplitudes (3a) and (3b) and neglecting the higher order terms in lel 2 :