Estudio de la Isotopología de Tsagas-Sourlas-Santilli

Abstract

Since his original proposal of 1978 to study Lie-isotopic and Lie-admissible liftings of conventional, local-differential Hamiltonian formulations of point particles, the physicist R. M. Santilli suggested the contribution of a new topology as the mathematical foundations for the representation of extended, nonspherical and deformable particles with conventional local-differential interaction plus new nonlocal-integral interation as occurring, for instance, in molecular valence bonds. A first isotopic lifting of the conventional continuity was introduced by the physicist J. V. Kadeisvili in 1992. In 1993 the mathematicians G. T. Tsagas and D. S. Sourlas built the topology proposed by Santilli within the context of isotopic mathematics defined over fields of conventional numbers. In the same year, Santilli constructed the fields isonumbers, namely numbers with a positive-definite but otherwise arbitrary multiplicative unit. As a necesary condition to achieve invariance of isotopic formulations under the action of their own time evolution group, Santilli extended in 1996 the topology of Tsagas and Sourlas to isofields whose unit is a sufficiently smooth and positive definite, but arbitrary integro-differential expression representing extended particles with local-differential and nonlocal-integral interations. This memoir is dedicated to the aparently first, comprehensive mathematical study and generalization of the Tsagas-Sourlas-Santilli isotopology and includes: a generalization of the Kadeisvili's isocontinuity; the identification of the broadest possible isofields and isomanifolds; the systematic study of the broadest possible isotopology; and other topics. It is hoped that the isotopology emerging from this study does indeed fulfill Santilli's original suggestion of constituting the foundations of mathematical, physical and chemical studies on isotopic representations of extended, nonspherical and deformable particles with local-differential and nonlocal-integral interactions.

En 1993, Tsagas y Sourlas definieron una isotopología en el caso en el que la proyección de un levantado isotópico de los números reales en el nivel convencional no coincida con dicho conjunto, es decir, en el caso en que se está trabajando con un isocuerpo de los denominado por Santilli de primer tipo. el propio Santilli también trató, en 1996, el caso de una isotopología para los llamados isocuerpos de segundo tipo. El objetivo principal de este artículo es profundizar en el estudio de esta segunda construcción, teniendo en cuenta los trabajados mencionados anteriormente de Tsagas, Sourlas y Santilli. Hemos optado para ello por definir un isoorden en el isocuerpo construido y realizar una generalización de la isocontinuidad de Kadeisvili para icuerpos de segundo tipo.