Studies of the Regular and Irregular Isorepresentations of the Lie-Santilli Isotheory

Muktibodh AS and Santilli R

Abstract

As it is well known, the Lie theory is solely applicable to dynamical systems consisting of point-like particles moving in vacuum under linear and Hamiltonian interactions (systems known as exterior dynamical systems). One of the authors (R.M. Santilli) has proposed an axiom-preserving broadening of the Lie theory, known as the Lie-Santilli isotheory, that is applicable to dynamical; systems of extended, non-spherical and deformable particles moving within a physical medium under Hamiltonian as well as non-linear and non-Hamiltonian interactions (broader systems known as interior dynamical systems). In this paper, we study apparently for the first time regular and irregular isorepresentations of Lie-Santilli isoalgebras occurring when the structure quantities are constants or functions, respectively. A number of applications to particle and nuclear physics are indicated. It should be indicated that this paper is specifically devoted to the study of isorepresentations under the assumption of a knowledge of the Lie-Santilli isotheory, as well as of the isotopies of the various branches of 20th century applied mathematics, collectively known as isomathematics, which is crucial for the consistent formulation and elaboration of isotheories.