AN INTRODUCTION TO IRREVERSIBLE LIE-ADMISSIBLE MATHEMATICS FOR CONTROLLED NUCLEAR FUSIONS
Ruggero Maria
Santilli1;
1HADRONIC TECHNOLOGIES CORPORATION, Palm Harbor, United States;
Type of Paper: Regular
Id Paper: 265
Topic: 38Abstract:
Studies in the axiomatic formulation of the irreversibility of nuclear fusions with the most general possible SA and NSA forces were initiated in the 1967 Ph. D. Thesis [1] [2] via the generalization of Lie algebras into Albert’s Lie-admissible and Jordan-admissible algebras [3] and the formulation of the first known deformations of Lie algebras with product (Eq. (8) of [1])
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which, twenty years later, were followed by tens of thousands of papers on q-deformations. In 1978, after joining the Department of Mathematics of Harvard University under DOE support, Santilli achieved [4] the axiomatic formulation of irreversibility via bi-modules in which motions forward (backward) in time are represented with the ordering of all products to the right (ordering of all products to the left)
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NQhHK4+LRLnqPiFIsdY/AL2PDgJ/QX7m3XW6pwnmjfUwbLRJtwnWKxozYeRMU/+rt7irFe+DeBFqv7ioUEd86mB7qtM9xraHcVh5NrHm8q9Pz9NDU+U5NnHlpOl7JwpjMrTxQCgoBMPksJSRaPsfAe8T0gMMBnwQpcpzlYWl0IFAKFQCFQCBQCsyNweUdFs+uCInAhUAgUAoVAIVAIYAn8D3fZVwtGlmu0AAAAAElFTkSuQmCC)
The Lie-admissible branch of hadronic mechanics [5] [6] (see also [7]-[17]) is then characterized by two inequivalent iso-mathematics, one per each direction of time, resulting in the Lie-admissible generalization of Heisenberg’s equation for an observable Q in the infinitesimal and finite forms in which SA interactions are represented by the Hamiltonian H and forward NSA interactions are represented by the Santillian S [1] [2]
![](data:image/png;base64,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)
![](data:image/png;base64,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)
where e> (e<) is the exponentiation in the forward (backward) iso-envelope, with particular case for R = 1 − F/H, S = 1
![](data:image/png;base64,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)
We then have the time rate of increase of the energy expected for nuclear fusions,
showing that Lagrange’s and Hamilton’s external terms F are represented by the Jordan algebra content of the Lie-admissible algebra. Note that given quantum mechanical models of nuclear fusions can be completed into hadronic models via four different simple non-unitary transformations
, with a consistent representation of irreversibility, the extended share of nuclear constituents and their broadest possible SA and NSA interactions. Applications to sustainable and controlled nuclear fusions are presented in Refs. [18] [19]. Tutoring lecture [20] are recommendable for physicists.
Keywords:
Hadronic Chemistry; Hadronic Mechanics; Mathematics; Santilli Iso- Geno- Hyper- And Isodual-Numbers
References:
[1] R. M. Santilli, ”Embedding of Lie-algebras into Lie-admissible algebras,” Nuovo Cimento 51, 570-585 (1967), www.santilli-foundation.org/docs/Santilli-54.pdf
[2] R. M. Santilli, ”Dissipativity and Lie-admissible algebras,” Meccanica 1, 3-12 (1969).
[3] A. A. Albert, Trans. Amer. Math. Soc. 64, 552-585 (1948).
[4] R. M. Santilli, ”Initiation of the representation theory of Lie-admissible algebras of operators on bimodular Hilbert spaces,” Hadronic J. 3, 440-467 (1979), http://www.santilli-foundation.org/docs/santilli-1978-paper.pdf
[5] R. M. Santilli, Lie-Admissible Approach to the Hadronic Structure, International Academic Press, Vols. I and II (1978), http://www.santilli-foundation.org/docs/santilli-71.pdf, http://www.santilli-foundation.org/docs/santilli-72.pdf
[6] R. M. Santilli, Elements of Hadronic Mechanics, Volumes I, II, III, Ukraine Academy of Sciences (1995), http://www.i-b-r.org/Elements-Hadronic-Mechanics.htm
[7] H. C. Myung and R. M. Santilli, Editors, Proceedings of the Second Workshop on Lie-Admissible formulations, Parts A and B: http://www.santilli-foundation.org/docs/hj-2-6-1979.pdf, http://www.santilli-foundation.org/docs/hj-3-1-1979.pdf
[8] H. C. Myung and R. M. Santilli, Editors, Proceedings of the Third Workshop on Lie-Admissible Formulations, Parts A, B, C: http://www.santilli-foundation.org/docs/hj-4-2-1981.pdf, http://www.santilli-foundation.org/docs/hj-4-3-1981.pdf, http://www.santilli-foundation.org/docs/hj-4-4-1981.pdf
[9] T. Arenas, J. Fronteau and R. M. Santilli, Editors, Proceedings of the First International Conference on Nonpotential Interactions and their Lie-Admissible Treatment, Part A, B, C, D: http://www.santilli-foundation.org/docs/hj-5-2-1982.pdf, http://www.santilli-foundation.org/docs/hj-5-3-1982.pdf, http://www.santilli-foundation.org/docs/hj-8-4-1982.pdf, http://www.santilli-foundation.org/docs/hj-5-5-1982.pdf
[10] H. C. Myung and R. M. Santilli, Editors, Proceedings of the First and Second Workshops on Hadronic Mechanics, http://www.santilli-foundation.org/docs/hj-6-6-1983.pdf, http://www.santilli-foundation.org/docs/hj-7-5-1984.pdf, http://www.santilli-foundation.org/docs/hj-7-6-1984.pdf
[11] Tuladhar Bhadra Man, Editor, Proceedings of the third international conference on the Lie-admissible treatment of non-potential interactions, Kathmandu University, Nepal (2011), Vol. I and II: 2 http://www.santilli-foundation.org/docs/2011-nepal-conference-vol-1.pdf, http://www.santilli-foundation.org/docs/2011-nepal-conference-vol-2.pdf
[12] A. Schoeber, Editor, Irreversibility and Non-potentiality in Statistical Mechanics, Hadronic Press (1984), http://www.santilli-foundation.org/docs/Santilli-110.pdf
[13] S. Beghella-Bartoli and R. M. Santilli, Editors, Proceedings of the 2020 teleconference on the Einstein-Podolsky-Rosen argument that ’Quantum mechanics is not a complete theory,” Curran Associates, New York, NY (2021), www.proceedings.com/59404.html
[14] J. Fronteau, A. Tellez-Arenas and R. M. Santilli, ”Lie-admissible structure of statistical mechanics,” Hadronic Journal 3, 130-176 (1979), http://www.santilli-foundation.org/docs/arenas-fronteau-santilli-1981.pdf
[15] J. Dunning-Davies, J. Dunning-Davies, ”The Thermodynamics Associated with Santilli’s Hadronic Mechanics,” Progress in Physics 4, 24-26 (2006), http://www.santilli-foundation.org/docs/Dunning-Davies-Thermod.PDF
[16] A. A. Bhalekar, ”Santilli’s Lie-Admissible Mechanics. The Only Option Commensurate with Irreversibility and Nonequilibrium Thermodynamics,” AIP Conf. Proc.
1558, 702-722 (2013), http://www.santilli-foundation.org/docs/bhalekar-lie-admissible.pdf
[17] T. Vougiouklis, ”The Santilli theory ’invasion’ in hyperstructures,” Algebras, Groups and Geometries 28, 83-104 (2011), http://www.santilli-foundation.org/docs/santilli-invasion.pdf
[18] R. M. Santilli, ”Lie-admissible invariant representation of irreversibility for matter and antimatter at the classical and operator levels,” Nuovo Cimento B 121, 443-485 (2006), http://www.santilli-foundation.org/docs//Lie-admiss-NCB-I.pdf
[19] R. M. Santilli, ”Apparent Resolution of the Coulomb Barrier for Nuclear Fusions Via the Irreversible Lie-admissible Branch of Hadronic Mechanics,” Progress in Physics, 18, 138-163 (2022), www.ptep-online.com/2022/PP-64-09.PDF
[20] R. M. Santilli, ”Tutoring on Lie-admissible mathematics,” Parts I, II, III: http://www.world-lecture-series.org/santilli-tutoring-iv-part-1, http://www.world-lecture-series.org/santilli-tutoring-iv-part-2, http://www.world-lecture-series.org/santilli-tutoring-iv-part-3Cite this article as:
Santilli R. (2023).
AN INTRODUCTION TO IRREVERSIBLE LIE-ADMISSIBLE MATHEMATICS FOR CONTROLLED NUCLEAR FUSIONS.
In 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
(Eds.), Sustainable Industrial Processing Summit
Intl. Symp on Physics, Mathematics and Multiscale Mechanics
(pp. 51-54).
Montreal, Canada: FLOGEN Star Outreach