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A solution of the inhomogeneous Bloch equation is given for a class of time-varying magnetic fields. A method of determining the fundamental system of the homogeneous Bloch equation employing the characteristics of the Riccati equation is formulated. It turns out that the fundamental matrix is an orthogonal matrix. A brief discussion of the characteristics of the magnetic field class and an illustrative example are given.

We demonstrate the complementary scheme for massive totally antisymmetric tensor field theories. The differential geometry plays a crucial role in this formulation

Quantization of the Rarita-Schwinger field interacting with the internal (external) electro­ magnetic field is made by using the Dirac-Casalbuoni method. The generators of the Poincare group are explicitly given when the electromagnetic field is quantized. The com­ mutator of the symmetric energy-momentum densities is also obtained. When the external electromagnetic field is coupled to the Rarita-Schwinger field, some of the constraint equations have explicit time-dependence. We develop the Dirac formalism for the system with time­ dependent constraints. The result turns out to be that the J ohnson-Sudarshan disease associated with the equal-time anti-commutation relations still exists, so far the electromagnetic field is coupled through the minimal interaction.

From the viewpoint that Regge behaviour is due to crossed channel exchanges, we discuss the infinite one-particle-exchange (lOPE) approach, especially a model which generates cuts in the direct channel variable s. At the present stage this model shows Regge behaviour locally in the small negative momentum transfer t region.

The implication of Regge asymptotic behaviour is studied on the basis of an infinite sum of one-particle-exchange (lOPE) amplitude, which provides a wide framework including vari­ ous versions of dual amplitudes. The imaginary part of Regge-behaved amplitude comes from the s-u crossing term of the convergent lOPE amplitude, accompanied with the diver­ gence of lOPE expression. Duality between t-poles and u- or s-singularities is necessarily contained in Regge behaviour. A general expression for the lOPE amplitude satisfying full Regge behaviour is persued and comments on related models are made in connection with our approach. Phenomenological aspects of various solutions are also discussed. The analysis of hadron scattering using finite energy sum rules has revealed the existence of an intimate connection between Regge pole exchanges and re­ sonant states in direct channel and has developed into Veneziano amplitude. This has created a problem of understanding of the physical implication of Regge pole exchanges. Regge pole exchange originally gave an exchange picture of composite par­ ticles at high energies. Its connection with the one-particle-exchange (OPE) mo­ del (which was proposed as an application to hadron reactions of the Sakata model) is quite interesting, especially when we consider its success in describ­ ing low energy scattering phenomena, such as nucleon-nucleon scattering. Among the interpretations of Regge behaviour so far proposed, that of an infinite sum of single exchanges of Regge recurrences is the most attractive one for a gener­ alization of OPE model. The purpose of the present paper is to give a general expression for the scattering amplitude based on the infinite sum of one-particle-exchange (lOPE) model/), 2 ) in which Regge behaviour is imposed at the asymptotic energy region. As an a posteriori result, the duality concept comes from the requirement of Regge behaviour in all the complex u plane except a positive real axis, where

Le champ de Rarita-Schwinger couple a un champ electromagnetique externe est reduit a un modele mecanique contraint. On montre que les paradoxes de Rarita-Schwinger sont vus comme des phenomenes generaux inherents aux systemes contraints

The recent Serpukhov data show that the forward slope of the elastic p-p differential cross sections increases with energy above 20 Ge V / c.1> The purpose of this note is to discuss a simple diffraction model which is capable of explaining such a shrinkage of the forward peaks. Let us assume that the aggregate of inelastic processes has, as far as their effects on the elastic process are concerned, some simple representation and can be effectively expressed by a two-body channel p + p where p is a hypothetical "isobar". In the following discussion we treat p and p as spinless particles. Assuming the dominance of the diffraction scattering for small momentum transfer elastic scattering, the partial wave S-matrix for elastic protonproton scattering may be written as2>