Tadao Nakano

A Relativistic Field Theory of an Extended Particle, I

Quantization of motion of a rigid body and its extension to the relativistic form are attempted here; The special· theory of relativtty ts believed that it rules the phenomena in the macroscopic world. But, so far, we do not know the rule which governs the microscopic world as the interior of an elementary particle. Here we .assume that the internal space of an elementary particle is Euclidean. The field equatiort, however, has the relattvisttcal!y mvariant form so that the expectation values of observable quantities become relattvistically covariant. The ccr.dition t\lat the time components of an internal angular momentum. have zero expectation values in the rest system leads to the general linear equation derived by Bhabha7l for elementary particles with arbitrary spins. When interactions are a!: sent, the solutions of die field equations are obtained and quantization of the field of a rigid sphere is done.

Possible Observation of the Skew-Symmetric Tensor Gauge Field

When we consider the translational gauge transformation for spinning particles, we need a vier-bein field in order to keep invariance of the theory. There is a possibility that a skew-symmetric tensor field appears by· a linear approximation and maintains its proper position in physical phenomena. We discuss how to find out effects by this new field. From elastic neutrino scattering experiments we will be able to discuss the existence of the skew-symmetric field. Though our purpose is to study the observational possibility of these fields, in this paper we restrict ourselves to investigate the field which is deduced from the requirement of the invariance under the extended translation only. Under linear approximation this gauge field is decomposed into a symmetric field sk~ and a skew-symmetric one A,~~· The former of which source is the symmetric energy-momentum tensor density is identified with the well-known gravitational field. On the other hand the latter of which source is the skew-symmetric one is classically unknown. Of course, magnitude of the universal coupling constant of this skew-symmetric field A1c~ is also unknown. We have no ground that its magnitude has to be of the same order as the one of the ordinary gravitational field Stu~· This does noJ deny a possibility of extreme difference between the fields Stu~ and ATG~ in magnitude of coupling constant, nor deny a further possibility that the coupling constant of the field Ak~ is so large that we may catch effects of this field in elementary processes in contrast to the ordinary gravitatinal field sk~·

On the Strong Interaction

A series of equations is proposed for the description of strong hyperon- meson interactions, in which the global symmetry theory is rejected. (D.L.C.)

Lorentz Gauge Field and Spin Angular-Momentum

On etudie la theorie de jauge qui est invariante sous translation locale et transformation de Lorentz intrinseque locale