AN INTRODUCTION TO REVERSIBLE LIE-ISOTOPIC MATHEMATICS FOR STABLE NUCLEAR STRUCTURES Ruggero Maria Santilli1; 1HADRONIC TECHNOLOGIES CORPORATION, Palm Harbor, United States; PAPER: 263/Mathematics/Plenary (Oral) OS SCHEDULED: 11:30/Tue. 28 Nov. 2023/Showroom ABSTRACT: We recall the experimental evidence according to which nuclei are composed by extended protons and neutrons in conditions of partial mutual penetration with ensuing interactions that are: linear, local and potential, thus variationally self-adjoint (SA) [1], as well as non-linear in the wave functions (as pioneered by W. Heisenberg), non-local because defined on volumes (as pioneered by L. de Broglie and D. Bohm) and non-derivable from a potential because of contact, thus zero range and variationally non-self-adjoint (NSA) type, as pioneered by R. M. Santilli in 1978 then at Harvard University under DOE support [1]. We then review the foundations of the time reversal invariant Lie-isotopic mathematics, also known as Santilli iso-mathematics, proposed in the volume [2] which is based on the preservation of the abstract axioms of 20th century applied mathematics and the use of their broadest possible realization, thus including the isotopy of [2]-[6]: 1) The quantum mechanical enveloping associative algebra of Hermitean operators ξ : {A, B, ...; AB = A × B, I} representing SA interactions via a Hamiltonian H(r, p) into the iso-associative enveloping algebra where References: [1] R. M. Santilli, Foundation of Theoretical Mechanics, Springer-Verlag, Heidelberg, Germany, Vol. I (1978), www.santilli-foundation.org/docs/Santilli-209.pdf<br />[2] R. M. Santilli, Foundation of Theoretical Mechanics, Springer-Verlag, Heidelberg, Germany, Vol. II (1983), www.santilli-foundation.org/docs/santilli-69.pdf<br />[3] R. M. Santilli, Elements of Hadronic Mechanics, Ukraine Academy of Sciences, Kiev, Vol. I (1995), Mathematical Foundations, http://www.santilli-foundation.org/docs/Santilli-300.pdf<br />[4] C.-X. Jiang, Foundations of Santilli Isonumber Theory, International Academic Press (2001), http://www.i-b-r.org/docs/jiang.pdf<br />[5] R. M. F. Ganfornina and J. N. Valdes, Fundamentos de la Isotopia de Santilli, International Academic Press (2001), English translation http://www.i-b-r.org/docs/Aversa-translation.pdf<br />[6] S. Georgiev, Foundations of IsoDifferential Calculus, Volumes 1 to 6, Nova Publishers, New York (2014-2016) and Iso-Mathematics, Lambert Academic Publishing (2022).<br />[7] R. M. Santilli and G. Sobczyk, Representation of nuclear magnetic moments via a Clifford algebra formulation of Bohm’s hidden variables, Scientific Reports 12, 1-10 (2022), http://www.santilli-foundation.org/Santilli-Sobczyk.pdf<br />[8] R. M. Santilli, ”Reduction of Matter in the Universe to Protons and Electrons via the Lie-isotopic Branch of Hadronic Mechanics,” Progress in Physics, Vol. 19, 73-99 (2023), http://www.ptep-online.com/2023/PP-65-09.PDF<br />[9] R. M. Santilli, ”Tutoring lecture on iso-mathematics,” http://www.world-lecture-series.org/santilli-tutoring-i |