2023-Sustainable Industrial Processing Summit
Intl. Symp on Physics, Mathematics and Multiscale Mechanics
| Editors: | F. Kongoli, A. B. Bhattacharya, A.C. Pandey, G. Sandhu, F. Quattrocchi, L. Sajo-Bohus, S. Singh, H.S. Virk, R.M. Santilli, M. Mikalajunas, E. Aifantis, T. Vougiouklis, P. Mandell, E. Suhir, D. Bammann, J. Baumgardner, M. Horstemeyer, N. Morgan, R. Prabhu, A. Rajendran |
| Publisher: | Flogen Star OUTREACH |
| Publication Year: | 2023 |
| Pages: | 298 pages |
| ISBN: | 978-1-989820-96-4 (CD) |
| ISSN: | 2291-1227 (Metals and Materials Processing in a Clean Environment Series) |
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AN INTRODUCTION TO REVERSIBLE LIE-ISOTOPIC MATHEMATICS FOR STABLE NUCLEAR STRUCTURES
Ruggero Maria Santilli1;1HADRONIC TECHNOLOGIES CORPORATION, Palm Harbor, United States;
Type of Paper: Plenary
Id Paper: 263
Topic: 38
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 
with iso-product 
, iso-unit 
and the Santillian 
for the representation of NSA interactions; 2) Lie’s theory into the Lie-Santilli iso-theory; 3) Numeric fields 
into Santilli iso-fields 
of iso-numbers 
; 4) Functional analysis into the iso-functional form; 5) Metric spaces 
over 
into iso-metric iso-spaces 
over 
and iso-metrics 
; 6) Newton-Leibnitz local differential calculus into a non-linear, non-local and NSA form with iso-differential 
; 7) Geometries on S over F into iso-geometries on isospaces 
over . Iso-mathematics characterizes the iso-mechanical branch of hadronic mechanics with Lie-isotopic generalization of Heisenberg equation for the time evolution of an observable 
in the infinitesimal and finite forms [2] [3]
where 
is the exponentiation in 
. It should be indicated that iso-mathematics and iso-mechanics can be constructed via the simple non-unitary transformation 
provided it is applied to the totality of conventional formalisms. We finally indicate that iso-mathematics and iso-mechanics have permitted the first and only known numerically exact and time invariant representation of experimental data for stable nuclei [7]-[8]. Tutoring lecture [9] may be a good introduction to iso-mathematics for physicists. A knowledge of this lecture is a necessary pre-requisite for the subsequent lecture on the broader, irreversible, Lie-admissible mathematics used for irreversible nuclear fusions.
Keywords:
Hadronic Chemistry; Mathematics; Santilli Iso- Geno- Hyper- And Isodual-NumbersReferences:
[1] R. M. Santilli, Foundation of Theoretical Mechanics, Springer-Verlag, Heidelberg, Germany, Vol. I (1978), www.santilli-foundation.org/docs/Santilli-209.pdf[2] R. M. Santilli, Foundation of Theoretical Mechanics, Springer-Verlag, Heidelberg, Germany, Vol. II (1983), www.santilli-foundation.org/docs/santilli-69.pdf
[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
[4] C.-X. Jiang, Foundations of Santilli Isonumber Theory, International Academic Press (2001), http://www.i-b-r.org/docs/jiang.pdf
[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
[6] S. Georgiev, Foundations of IsoDifferential Calculus, Volumes 1 to 6, Nova Publishers, New York (2014-2016) and Iso-Mathematics, Lambert Academic Publishing (2022).
[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
[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
[9] R. M. Santilli, ”Tutoring lecture on iso-mathematics,” http://www.world-lecture-series.org/santilli-tutoring-i