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THE BARYCENTER IN THE FUNCTIONAL THEORY OF PARTICLE SYSTEMS

Florence A. Aeschlimann

Published Feb 1, 1960• 0 citations
OpenAlex

Abstract

A definition is given of the barycentric wave for a system of n particles in the functional theory, in the relativistic case, and in the non- relativistic case with spin and isospin or without spin. The equation for the barycentric wave in the relativistic case and in the non-relativistic case is derived. The case of particles of the same mass is considered. Motion around the barycenter is discussed, and equations for the relative motion are obtained. The particular case of a two-particle system is considered. (auth)

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Compt. rend.•Jan 1, 1960•0 citations
A definition is given of the barycentric wave for a system of n particles in the functional theory, in the relativistic case, and in the non- relativistic case with spin and isospin or without spin. The equation for the barycentric wave in the relativistic case and in the non-relativistic case is derived. The case of particles of the same mass is considered. Motion around the barycenter is discussed, and equations for the relative motion are obtained. The particular case of a two-particle system is considered. (auth)
A study is made of a system of two particles with spin in relativistic functional theory. Equation of the barycentric wave, equations of the relative motion, and the reduced equation are obtained. In the states of the system, in some cases there exist states where the relative waves are constants. This case corresponds to vanishing relative motion. In the case of two particles of spin 1/ 2 of the same mass, a fused system is obtained which is equivalent to a particle with spin 1. From this result, by the approximation giving the usual wave mechanics, the equations given by the fusion method are obtained. The fusion method is thus justified and its physical significance is apparent. (auth.)
A study was made of the general conditions required to set up a non- relativistic functional theory for systems of particles. Representation of each particle of a system by a space-time function uj(P,T). Formal classification for the particles of the system with respect to indiscernability and the exclusion principle for the fermions. Using the general theory of predictions, the arguments of the functional for predictions are fixed, functional configuration- space is introduced, and the general form of the equation for the predictional elements is determined. Conditions incurred by the limiting cases of the usual wave mechanics for systems and of the single particle in the functional theory of particles. Fundamental principle for the equations of motion concerning the particles of a system: each function uj(P,T) describing a particle of the system obeys a non-linear equation which depends upon the functions u/sub k/(P,T) of the other particles of the system. Brief investigation of the limiting case of classical mechanics. (auth)