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Transcript
Eighth International Conference on Geometry, Integrability and Quantization June 9–14, 2006, Varna, Bulgaria Ivaïlo M. Mladenov and Manuel de León, Editors SOFTEX, Sofia 2007, pp 302–311 A GEOMETRIC MODEL FOR EXTENDED PARTICLES ABDALLAH SMIDA, AMEH HAMICI and MAHMOUD HACHEMANE Faculté de Physique, USTHB, BP. 32 El-Alia Bab-Ezzouar Alger, Algeria Abstract. Here we combine the ideas of a quantum functional theory intended to describe intrinsically extended particles with those of a geometrostochastic one describing stochastically extended particles. The main ingredients of the former are a physical wave u replacing the point x and a functional wave X[u, t] replacing the probability wave function of the conventional quantum theory. The latter introduces a proper wave function accounting for the unavoidable errors in the measurement of continuous observable such as the position and momentum. 1. Introduction In the nineteen fifties of previous century, Destouches [1, 2] developed his functional quantum theory as a generalization of de Broglie’s theory. His basic idea was that elementary particles need not be pointlike. Being extended and non rigid is a better conception. Rather than conceiving the particle as a bulk of fluid, we have supposed that it is composed of pointlike quantum modes. This enabled the construction of our Geometro-Differential Model (G-D-M) for extended particles and its quantization by a method of induced representation [3, 4, 9, 10]. The geometric structure have been drawn from a recent Geometro-Stochastic Theory (G-S-T) which seems to be a candidate for the unification of quantum mechanics and general relativity devoid of many of the inconsistencies of both theories [6–8]. It deals with an extension of particles attributed to the impossibility of sharply measuring a position (or momentum) of a particle. It is a stochastic extension. The aim of the present work is to describe a scheme of the extended particles which incorporate both the intrinsic and stochastic extensions. To achieve this, we shall combine our G-D-M with the G-S-T. 302
