Abstract
As it is well known, 20th century applied mathematics with related physical and chemical theories, are solely applicable to point-like particles moving in vacuum under Hamiltonian interactions (exterior dynamical problems). In this note, we study the covering of 20th century mathematics discovered by R. M. Santilli, today known as Santilli isomathematics, representing particles as being extended, non-spherical and deformable while moving within a physical medium under Hamiltonian and non-Hamiltonian interactions (interior dynamical problems). In particular, we focus the attention on a central part of isomathematics given by the isorepresentations of the Lie-Santilli isoalgebras that have been classified into regular (irregular) isorepresentations depending on whether the structure quantities of the isocommutation rules are constants (functions of local variables). The importance of the study of the isorepresentation theory for a number of physical and chemical applications is pointed out
Highlights
As it is well known, 20th century applied mathematics at large, and the Lie theory in particular, can only represent point-like particles moving in vacuum, resulting in a body of methods that have proved to be effective whenever particles can be effectively abstracted as being point-like, such as for the structure of atoms, and crystals, particles moving in accelerators, and many other systems
It is well known that point-like abstractions of particles are excessive for extended, non-spherical and deformable particles moving within a physical medium, as it is the case for the structure of hadrons, nuclei and stars since their constituents are in a state of mutual penetration of their wavepackets and/or charge distribution
An important feature of the finite size of particles in interior conditions is that they experience conventional action-a-distance, Hamiltonian interactions, as well as additional contact, non-potential and, non-Hamiltonian interactions, with the consequential inapplicability of 20th century applied mathematics at large, and of Lie’s theory in particular
Summary
As it is well known, 20th century applied mathematics at large, and the Lie theory in particular, can only represent point-like particles moving in vacuum (exterior dynamical problems), resulting in a body of methods that have proved to be effective whenever particles can be effectively abstracted as being point-like, such as for the structure of atoms, and crystals, particles moving in accelerators, and many other systems. It should be indicated that Santilli’s pioneering works signal the historical transition from the notion of massive point, introduced by Newton, and adopted by Galileo and Einstein, to a new generation of physical and chemical theories representing particles as they are in the physical or chemical reality. This historical advance has so many implications for all of quantitative sciences that it has been referred to as characterizing New Sciences for a New Era in the title of Ref. This historical advance has so many implications for all of quantitative sciences that it has been referred to as characterizing New Sciences for a New Era in the title of Ref. [21]
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
