Takehiko Takabayasi

Relativistic Hydrodynamics of the Dirac Matter. Part I. General Theory

The hydrodynamical model of Dirac matter is formulated and clarified. The basic equations are cast in various forms. Some characteristic features of the hydrodynamics are the distinctions between proper mass density and rest particle density and also between particle momentum and velocity, primarily specified by the theta behaviors. The energy-momentum conservation law also manifests a new structure. This quantum effect is interpreted as mechanical stress and flow of heat taking place inside the fluid. The theory provides a new directly physical point of view concerning various transformation properties of the Dirac field. Furthermore it reveals a conspicious quasisymmetrical property of the Dirac field existing between velocity and spin. The theory is formulated for cases of Dirac matter under external electromagnetic field and also of interacting Dirac and electromagnetic fields. It is manifestly gage-independent in both cases. The theory is worked out only for the case of c-number Dirac field. The mathematical method is systematized to estublish how the Dirac field can be manipulated solely with the set of tensor quantities which are related to the Dirac spinor as its bilinear covariants. (N.W.R.)

Relativistic Hydrodynamics Equivalent to the Dirac Equation

In our previous articles the hydrodynamical structures of the wave equations in quantum mechanics or field theory have been investigated in detail for the cases of relativistic scalar equation1> (Klein-Gordon equation) on the one hand and of non-relativistic spinor equation2> on the other. As was remarked there2>, a similar method can be applied to the case of Dirac wave equation. For this purpose we must first consider the kinematical problem to find out the set of tensor quantities under suitable subsidiary conditions which represents the Dirac spinor 1/J in a physically meaningful way. As such quantities we first take up the 16 density functions,

Theory of Relativistic Rotators and Elementary Particles. I

To supply a unified model of elementary particles, the theory of relativistic rotators is developed. Clarifying the physical concept of relativistic rotators, general theory is constructed on the basis of kinematical variables. Consideration of the physical properties of the internal rotational space leads to the definition of isospin and internal chirality. Other internal constants of motion are also taken out to be identified as mass and ordinary spin. Possible rotator models are classified according to the structure of the rotational part of the lagrangian. Various hitherto known models are automatically reproduced in ihis way, with their internal properties revealed. In addition, entirely new models follow from this scheme (auth)

Mass Rules for Baryons and Resonant States

The formula that expresses the baryon mass in terms of internal quantum numbers is generalized so as to apply to the low-lying baryon resonances. Simple relations that systematize masses of all other known baryon resonant states are also presented. (C.E.S.)

Theory of a One-Dimensional Relativistic Elastic Continuum and Hadronic Wave Equation

After Nambu and others derived the dual amplitude based on a string-like model,1 we derived the relativistic quantum mechanics of a finite one-dimensional elastic continuum (“string”), taken as a model of hadrons, by a “detailed wave equation“.2 We want here to reconstruct the theory by first giving the classical theory of a relativistic string and then quantizing it,3 in such a way that the method clarifies some general points which will be applicable to any more general relativistic extended model.4