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Studies on A. Einstein , B. Podolsky and N. Rosen argument that ”quantum mechanics is not a complete theory,” I: Basic methods
Abstract
In 1935, A. Einstein expressed his view, jointly with B. Podolsky and N. Rosen, that ”quantum mechanics is not a complete theory” (EPR argument). Following decades of preparatory studies, R. M. Santilli published in 1998 a paper showing that the objections against the EPR argument are valid for point-like particles in vacuum (exterior dynamical systems), but the same objections are inapplicable (rather than being violated) for extended particles within hyperdense physical media (interior dynamical systems) because the latter systems appear to admit an identical classical counterpart when treated with the isotopic branch of hadronic mathematics and mechanics. In a more recent paper, Santilli has shown that quantum uncertainties of extended particles appear to progressively tend to zero when in the interior of hadrons, nuclei and stars, and appear to be identically null at the limit of gravitational collapse, essentially along the EPR argument. In this first paper, we review, upgrade and specialize the basic mathematical, physical and chemical methods for the study of the EPR argument. In two subsequent papers, we review the above results and provide specific illustrations and applications.
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A. Einstein, B. Podolsky and N. Rosen, “Can quantum-mechanical description of physical reality be considered complete?” Phys. Rev., Vol. 47, p. 777 (1935), www.eprdebates.org/docs/epr-argument.pdf
N. Bohr, “Can quantum mechanical description of physical reality be considered complete?” Phys. Rev. Vol. 48, p. 696 (1935), www.informationphilosopher.com/solutions/scientists/bohr/EPRBohr.pdf
J.S. Bell: “On the Einstein Podolsky Rosen paradox” Physics Vol. 1, 195 (1964),www.eprdebates.org/docs/j.s.bell.pdf
J. von Neumann, Mathematische Grundlagen der Quantenmechanik,Springer, Berlin (1951).
D. Bohm, Quantum Theory, Dover, New Haven, CT (1989).
Stanford Encyclopedia of Philosophy, “bell’s Theorem” (first published 2005, revised 2019) https://plato.stanford.edu/entries/bell- theorem/
R. M. Santilli, “Isorepresentation of the Lie-isotopic SU(2) Algebra with Application to Nuclear Physics and Local Realism,” Acta Applicandae Mathematicae Vol. 50, 177 (1998), www.eprdebates.org/docs/epr-paper-i.pdf
R. M. Santilli, “Studies on the classical determinism predicted by A. Einstein, B. Podolsky and N. Rosen,”www.eprdebates.org/docs/epr-paper-ii.pdf
J. L. Lagrange, Mecanique Analytique (1788), reprinted by Gauthier- Villars, Paris (1888).
W. R. Hamilton, On a General Method in Dynamics (1834), reprinted in Hamilton’s Collected Works, Cambridge Univ. Press (1940).
A.A. Albert, Trans. Amer. Math. Soc. 64, 552 (1948).
R. M. Santilli, “Embedding of Lie-algebras into Lie-admissible algebras,” Nuovo Cimento 51, 570 (1967),www.santilli-foundation.org/docs/Santilli-54.pdf
A. U. Klimyk and R. M. Santilli, “Standard isorepresentations of isotopic Q- operator deformations of Lie algebras,” Algebras, Groups and Geometries 10 [1993], 323-333.
R. M. Santilli, “Dissipativity and Lie-admissible algebras,” Meccanica 1, 3 (l969).
R. M. Santilli, “An introduction to Lie-admissible algebras,” Suppl. Nuovo Cimento, 6, 1225 (1968).
R. M. Santilli, “On a possible Lie-admissible covering of Galilei’s relativity in Newtonian mechanics for nonconservative and Galilei form- non-invariant systems,” Hadronic J. Vol. 1, pages 223-423 (1978), www.santilli-foundation.org/docs/Santilli-58.pdf
R. M. Santilli, “Need of subjecting to an experimental verification the validity within a hadron of Einstein special relativity and Pauli exclusion principle,” Hadronic J. Vol. 1, pages 574-901 (1978),www.santilli-foundation.org/docs/santilli-73.pdf
R. M. Santilli, Foundation of Theoretical Mechanics, Springer-Verlag, Heidelberg, Germany, Volume I (1978) The Inverse Problem in Newtonian Mechanics, www.santilli-foundation.org/docs/Santilli-209.pdf
R. M. Santilli, Foundation of Theoretical Mechanics, Springer-Verlag, Heidelberg, Germany, Vol. II (1982) Birkhoffian Generalization of Hamiltonian Mechanics, www.santilli-foundation.org/docs/santilli-69.pdf
R. M. Santilli, “Initiation of the representation theory of Lie- admissible algebras of operators on bimodular Hilbert spaces,” Hadronic J. Vol. 3, p. 440-506 (1979).
R. M. Santilli, “An introduction to the Lie-admissible treatment of nonpotential interactions in Newtonian, statistical and particle mechanics,” Hadronic J. Vol. 5,[264-359] (1982).
R. M. Santilli, Lie-Admissible Approach to the Hadronic Structure, Vol. I Non-Applicability of the Galileo and Einstein Relativities? Hadronic Press (1982),www.santilli-foundation.org/docs/santilli-71.pdf
R. M. Santilli, Lie-Admissible Approach to the Hadronic Structure, Vol. II Covering of the Galileo and Einstein Relativities? Hadronic Press (1982),www.santilli-foundation.org/docs/santilli-72.pdf
R. M. Santilli, “Lie-admissible invariant representation of irreversibility for matter and antimatter at the classical and operator levels,” Nuovo Cimento B 121, 443 (2006),www.i-b-r.org/Lie-admiss-NCB-I.pdf
R. M. Santilli, “An introduction to the new sciences for a new era,” Invited paper, SIPS 2016, Hainan Island, China Clifford Analysis, Clif- ford Algebras and their Applications Vol. 6, No. 1, p. 1-119, 2017, www.santilli-foundation.org/docs/new-sciences-new-era.pdf
R. M. Santilli. “The novel “Controlled Intermediate Nuclear Fusion: A report on its industrial realization as predicted by hadronic mechanics,” Hadronic J. Vol. f 31, p. 1-65, (2008),www.i-b-r.org/CNF-printed.pdf
R. Brenna, T. Kuliczkowski, L. Ying, “Verification of Santilli intermediate Controlled Nuclear Fusions without harmful radiations and the production of magnecular clusters,” New Advances in Physics, Vol. 5, p. 9-76 (2011),www.santilli-foundation.org/docs/ICNF-2.pdf
J. V. Kadeisvili, C. Lynch and Y. Yang, “Confirmations of Santilli Intermediate Nuclear Fusions of Deuteron and Carbon into Nitrogen without Radiations.” The Open Physical Chemistry Journal Vol. 5, p. 17026 (2013),www.santilli-foundation.org/docs/ICNF-Conf-2013.pdf
R. M. Santilli, “Experimentally evidence on the synthesis of Silicon from Oxygen and Carbon without harmful radiation or waste,” Proceedings of the Third International Conference on the Lie-Admissible Treatment of Irreversible Processes, Kathmandu University pages 163-177 (2011), http://www.santilli-foundation.org/docs/ICNF-3.pdf
R. M. Santilli, “Additional Confirmation of the Intermediate Controlled Nuclear Fusions without harmful radiation or waste,” in the Proceedings of the Third International Conference on the Lie-Admissible Treatment of Irreversible Processes, Kathmandu University p. 163-177(2011),www.santillifoundation.org/docs/ICNF-3.pdf
R. M. Santilli, 10 minutes DVD on the “Operation of the Hadronic Reactor III for the synthesis the Silicon,”www.world-lecture-series.org/dragon-iii
R. M. Santilli “The sound of Intermediate Controlled Nuclear Fusions,”www.santilli-foundation.org/Thunder-Fusions.amr
U. Abundo, “Interpretation and enhancement of the excess energy of Rossi’s reactor via Santilli neutroids and nucleoids,” Hadronic Journal Vol. 37, p. 697-737 (2014), www.thunder-fusion.com/docs/abundo-paper-2014.pdf
L. Ying, W. Cai, J. , C. Lynch, S. Marton, S. Elliot and Y. Yang, “Experimental verification for Intermediate Controlled Nuclear Fusion,” City College of New York, Preprint to appear,www.santilli-foundation.org/docs/ICNF-Cai-paper- Ying.pdf
L. Ying, “Verification of Santilli Intermediate Nuclear Harmful, Hadronic Journal Vol. 20, p. 45-561 (2005).
L. Ying, “Verification of Santilli Intermediate Nuclear Harmful Radiation and the Production of Magnecular Clusters,” Lecture VD of the website, www.world-lecture-series.org/level-v
R. B. Lanjewar, “A Brief Review of Intermediate Controlled Nuclear Syntheses (ICNS) without Harmful Radiations,” AIP Conference Proceedings 1648, 510012 (2015); doi: 10.1063/1.4912717,www.santilli-foundation.org/docs/1.4912717(RB-Lanjewar).pdf
Chandrakant S. Burande, “On the Rutherford-Santilli Neutron Model,” AIP Conference Proceedings 1648, 510006 (2015); doi: 10.1063/1.4912711, www.santilli-foundation.org/docs/1.4912711(CS-Burande(1)).pdf
Indrani B. Das Sarma, “Hadronic Nuclear Energy: An Approach Towards Green Energy,” AIP Conference Proceedings 1648, 510008 (2015); doi: 10.1063/1.4912713, www.santilli-foundation.org/docs/1.4912713(IB-Das Sarma).pdf
Sudhakar S. Dhondge, “Santilli’s Hadronic Mechanics of Formation of Deuteron,” AIP Conference Proceedings 1648, 510009 (2015); doi: 10.1063/1.4912714, www.santilli-foundation.org/docs/1.4912714(SS-Dhondge).pdf
D. Rossiter, Director, “IVA Report 184443 on comparative Nitrogen,” www.santilli-foundation.org/docs/IVAReport-184443.pdf
D. Rossiter, Director, “IVA Report 184445 on comparative Nitrogen counts on samples of the Nitrogen synthesis,” www.santillifoundation.org/docs/Spectral-analysis-Ref-[79].png
R. Brenna, T. Kuliczkowski and L. Ying, “Report on Test for Silicon on the Nitrogen synthesis,”www.santilli-foundation.org/docs/PGTI-Anal-test1.pdf
D. Rossiter, Director, “IVA Report 189920 on comparative Silica counts,”www.santilli-foundation.org/docs/IVAReport 189920.pdf
D. Rossiter, Director, “IVA Report 189920 on comparative Silica counts,” oxygen synthesis,www.santilli-foundation.org/docs/IVAReport 189920.pdf
D. Rossiter, “IVA Report 200010 on comparative Nitrogen counts,” www.santilli-foundation.org/docs/Oneida-analyses- 2013.zip
R. Brenna, T. Kuliczkowski, L. Ying, “Verification of Santilli intermediate Controlled Nuclear Fusions without harmful radiations and the production of magnecular clusters,” New Advances in Physics, Vol. 5, p. 9 (2011), www.santilli-foundation.org/docs/ICNF-2.pdf
D. Swartz, “Constellation Technologies first report on comparative Silica counts,”www.santilli-foundation.org/docs/Constellation-Si-10-13.zip
D. Swartz, “Constellation technologies second report on comparative Silica counts,”www.santilli-foundation.org/docs/Constellation-Rep-Si- 2.zip
D. Swartz, “Constellation technologies Third report on comparative Silica counts,”www.santilli-foundation.org/docs/Constell-Si-3.pdf
A. Nas, “Data on Constellation technologies tests 1 and 2 on comparative Silica counts,”www.santilli-foundation.org/docs/Data-Constelltests.docx
D. Swartz, “Constellation technologies Third report on comparative Silica counts,”www.santilli-foundation.org/docs/Constell-Silicon-10-14.pdf
R. M. Santilli, “The Novel Hyper Combustion for the Complete Combustion of Fossil Fuels”, Intern. Journal of Chemical Engineering and Applications, Vol. 10, p. 16-23, (2019),www.santilli-foundation.org/docs/hypercombustion-2019.pdf
R. Anderson, “Outline of Hadronic Mathematics, Mechanics and Chemistry as Conceived by R. M. Santilli,” Special Issue III: Foundations of Hadronic Mathematics, Mechanics and Chemistry, American Journal of Modern Physics Bol. 6, p. 1 -16 (2016),www.santilli-foundation.org/docs/HMMC-2017.pdf
R. M. Santilli, Elements of Hadronic Mechanics, Ukraine Academy of Sciences, Kiev, Volume I (1995), Mathematical Foundations, www.santilli-foundation.org/docs/Santilli-300.pdf
R. M. Santilli, Elements of Hadronic Mechanics, Ukraine Academy of Sciences, Kiev, Volume II (1994), Theoretical Foundations,www.santilli-foundation.org/docs/Santilli-301.pdf
R. M. Santilli, Elements of Hadronic Mechanics, Ukraine Academy of Sciences, Kiev, Volume III (2016), Experimental verifications, www.santilli-foundation.org/docs/elements-hadronic-mechanics- iii.compressed.pdf
R. M. Santilli, Isorelativities, International Academic Press, (1995).
R. M. Santilli, The Physics of New Clean Energies and Fuels According to Hadronic Mechanics, Special issue of the Journal of New Energy, 318 pages (1998),www.santilli-foundation.org/docs/Santilli-114.pdf
R. M. Santilli, Foundations of Hadronic Chemistry, with Applications to New Clean Energies and Fuels, Kluwer Academic Publishers (2001), www.santilli-foundation.org/docs/Santilli-113.pdf,Russian translation by A. K. Aringazin,www.i-b-r.org/docs/Santilli-Hadronic-Chemistry.pdf
R. M. Santilli, Hadronic Mathematics, Mechanics and Chemistry, Volumes I to V, International Academic Press, (2008),www.i-b-r.org/Hadronic-Mechanics.htm
H. C. Myung, Editor, Mathematical Studies on Lie-admissible Algebras,Volumes I, II, III, IV, and V, Hadronic Press (1985-1987).
A. Schoeber, Editor, Irreversibility and Non-potentiality in Statistical Mechanics, Hadronic Press (1984),www.santilli-foundation.org/docs/Santilli-110.pdf
M. L. Tomber, “A short history of nonassociative algebras,” Hadronic J. Vol. 2, p.11252-1387 (1979).
J. Fronteau, A. Tellez-Arenas and R. M. Santilli, “Lie-admissible structure of statistical mechanics,” Hadronic J. Vol. 3, p. 130-176 (1979).
J. A. Kobussen, “Lie-admissible structure of classical field theory,” Hadronic J. Vol. 3, p. 79-129 (1979).
R. H. Ohemke, “Some elementary structure theorems for a class of Lie-admissible algebras,” Hadronic J. Vol. 3, p. 293-219 (1979).
S. Okubo, Hadronic J. Vol. 5, p. 1667-1672 (1982).
Y. Ilamed, “On realizations of infinite-dimensional Lie-admissible algebras,” Hadronic J. Vol. 3, 327-338 (1979).
A. Jannussis, “Noncanonical quantum statistical mechanics,” Hadronic J. Suppl. Vol. 1, p. 576-609 (1985).
A. Jannussis and R. Mignani, “Algebraic structure of linear and non- linear models of open quantum systems,” Physica A Vol. 152, p. 469- 476 (1983).
D. Schuch, “Nonunitary connection between explicitly time-dependent and nonlinear approaches for the description of dissipative quantum systems,” Phys. Rev A Vol. 55, p. 955-966 (1997).
A. Bhalekar, “Santilli’s Lie-Admissible Mechanics. The Only OptionCommensurate with Irreversibility and Nonequilibrium Thermodynamics,” AIP Conference Proceedings 1558, 702 (2013); doi: 10.1063/1.4825588,www.santilli-foundation.org/docs/bhalekar-lie-admissible.pdf
T. Vougiouklis, “The Santilli theory ’invasion’ in hyperstructures,” Algebras, Groups and Geometries Vol. 28, pages 83-104 (2011), www.santilli-foundation.org/docs/santilli-invasion.pdf
A. K. , A. Jannussis, F. Lopez, M. Nishioka and B. Veljanosky, Santilli’s Lie-Isotopic Generalization of Galilei and Einstein Relativities, Kostakaris Publishers, Athens, Greece (1991),www.santilli-foundation.org/docs/Santilli-108.pdf
D. S. Sourlas and G. T. Tsagas, Mathematical Foundation of the Lie- Santilli Theory, Ukraine Academy of Sciences (1993),www.santilli-foundation.org/docs/santilli-70.pdf
J. Lohmus, E. Paal, and L. Sorgsepp, Non-associative Algebras in Physics, Hadronic Press, Palm Harbor, (1994),www.santilli- foundation.org/docs/Lohmus.pdf
J. V. Kadeisvili, Santilli Isotopies of Contemporary Algebras, Geometries and Relativities, Ukraine Academy of Sciences, Second edition (1997), www.santilli-foundation.org/docs/Santilli-60.pdf
Chun-Xuan Jiang, Foundations of Santilli Isonumber Theory, International Academic Press (2001),www.i-b-r.org/docs/jiang.pdf
Raul M. Falcon Ganfornina and Juan Nunez Valdes, Fundamentos de la Isdotopia de Santilli, International Academic Press (2001),www.i-b-r.org/docs/spanish.pdfEnglish translation: Algebras, Groups and Geometries Vol. 32, p. 135- 308 (2015), www.i-b-r.org/docs/Aversa-translation.pdf
Bijan Davvaz and Thomas Vougiouklis, A Walk Through Weak Hyper- structures and Hv-Structures, World Scientific (2018)
I. Gandzha and J. Kadeisvili, New Sciences for a New Era: Mathematical, Physical and Chemical Discoveries of Ruggero Maria Santilli, Sankata Printing Press, Nepal (2011), www.santilli-foundation.org/docs/RMS.pdf
S. Georgiev, Foundation of the IsoDifferential Calculus, Volume I, to VI, r (2014 on). Nova Academic Publishers.
H. Rutherford, Proc. Roy. Soc. A, Vol. 97, 374 (1920).
R. Norman and J. Dunning-Davies, “Hadronic paradigm assessed: neutroid and neutron synthesis from an arc of current in hydrogen gas,” Hadronic Journal Vol. 40, p. 119 - 140 (2017),www.santilli-foundation.org/docs/norman-dunningdavies- hj.pdf
R. M. Santilli, “Apparent consistency of Rutherford’s hypothesis on the neutron as a compressed hydrogen atom, Hadronic J. Vol. 13, p. 513-542 (1990),www.santilli-foundation.org/docs/Santilli-21.pdf
R. M. Santilli, “Apparent consistency of Rutherford’s hypothesis on the neutron structure via the hadronic generalization of quantum mechanics - I: Nonrelativistic treatment”, ICTP communication IC/91/47 (1992), www.santilli-foundation.org/docs/Santilli-150.pdf
R. M. Santilli, “On the relativistic synthesis of the neutron from the hydrogen atom,” Communication of the Joint Institute for Nuclear Research, Dubna, Russia, No. E4-93-252 (1993).
R. M. Santilli, “Recent theoretical and experimental evidence on the synthesis of the neutron,” Chinese J. System Eng. and Electr. Vol. 6, 177-186 (1995),www.santilli-foundation.org/docs/Santilli-18.pdf
R. M. Santilli, “Confirmation of Don Borghi’s experiment on the syn- thesis of neutrons,” arXiv publication, August 15, 2006, www.arxiv.org/pdf/physics/0608229v1.pdf
R. M. Santilli, “Apparent confirmation of Don Borghi’s experiment on the laboratory synthesis of neutrons from protons and electrons, Hadronic J. Vol. 30, p. 29032 (2007),www.i-b-r.org/NeutronSynthesis.pdf
R. M. Santilli and A. Nas, “Confirmation of the Laboratory Synthesis of Neutrons from a Hydrogen Gas,” Journal of Computational Methods in Sciences and Engineering Vol. 14 , 405-41 (2014), www.hadronictechnologies.com/docs/neutron-synthesis-2014.pdf
R. Norman, S. Beghella Bartoli, B. Buckley, J. Dunning-Davies, J. Rak, R. M. Santilli “Experimental Confirmation of the Synthesis of Neutrons and Neutroids from a Hydrogen Gas, American Journal of Modern Physics, Vol. 6, p.85-104 (2017),www.santilli-foundation.org/docs/confirmation-neutron-synthesis- 2017.pdf
J. V. Kadeisvili, “The Rutherford-Santilli Neutron,” Hadronic J. Vol. 31, p. 1-125, (2008),www.i-b-r.org/Rutherford-Santilli-II.pdf also available in in html format at www.i-b-r.org/Rutherford-Santilli-neutron.htm
C. S. Burande, “Santilli Synthesis of the Neutron According to Hadronic Mechanics,” American Journal of Modern Physics Vo l. 5, p. 17-36 (2016),www.santilli-foundation.org/docs/pdf3.pdf
J. M. Blatt and V. F. Weisskopf, Theoretical Nuclear Physics, John Wiley and Sons (1952).
R. M. Santilli, “A quantitative isotopic representation of the deuteron magnetic moment,” in Proceedings of the International Symposium ’Dubna Deuteron-93, Joint Institute for Nuclear Research, Dubna, Russia (1994), www.santilli-foundation.org/docs/Santilli-134.pdf
R. M. Santilli, “Nuclear realization of hadronic mechanics and the exact representation of nuclear magnetic moments,” Journal of Phys. Vol. 4, p. 1-70 (1998),www.santilli-foundation.org/docs/Santilli-07.pdf
R. M. Santilli, “Apparent Experimental Confirmation of Pseudo- protons and their Application to New Clean Nuclear Energies,” International Journal of Applied Physics and Mathematics Vol. 9, p. 72-100 (2019), www.santilli-foundation.org/docs/pseudoproton-verification- 2018.pdf
A. A. Bhalekar and R. M. Santilli, “Exact and Invariant representation of nuclear magnetic moments and spins according to hadronic mechanics,” American Journal of Modern Physics Vol. 5, p. 56-118 (2016),www.santilli-foundation.org/docs/nuclear-MM-spins.pdf
A. O. E. Animalu and R. M. Santilli, “Nonlocal isotopic representation of the Cooper pair in superconductivity,” Intern. J. Quantum Chemistry Vol. 29, p. 185-202 (1995), www.santilli-foundation.org/docs/Santilli-26.pdf
A. O. E. Animalu, Isosuperconductivity: A nonlocal-non hamiltonian theory of pairing in high Tc superconductivity, Hadronic J. Vol. 17, p. 349-428 (1984).
R. M. Santilli and D. D. Shillady,, “A new isochemical model of the hydrogen molecule,” Intern. J. Hydrogen Energy Vol. 24, p. 943-956 (1999),www.santilli-foundation.org/docs/Santilli-135.pdf
R. M. Santilli and D. D. Shillady, “A new isochemical model of the water molecule,” Intern. J. Hydrogen Energy Vol. 25, p. 173-183 (2000), www.santilli-foundation.org/docs/Santilli-39.pdf
Vijay M. Tangd, “Advances in hadronic chemistry and its applications,” Foundation of Chemistry, DOI 10.1007/s10698-015-9218-z (March 24, 2015),www.santilli-foundation.org/docs/hadronic-chemistry-FC.pdf
A. A. Bhalekar, R. M. Santilli, “Two Body IsoElectronium Model of the Heliumic System,” Special Issue III: Foundations of Hadronic Mathematics, Mechanics and Chemistry, American Journal of Modern Physics Vol. 6, p. 29-45 (2017),www.santilli-foundation.org/docs/bhalekar-santilli-isohelium.pdf
R. M. Santilli, “Isonumbers and Genonumbers of Dimensions 1, 2, 4, 8, their Isoduals and Pseudoduals, and ”Hidden Numbers,” of Dimension 3, 5, 6, 7,” Algebras, Groups and Geometries Vol. 10, p. 273-295 (1993),www.santilli-foundation.org/docs/Santilli-34.pdf
A. K. Aringazin,“Studies on the Lie-Santilli IsoTheory with Unit of general Form,” Algebras, Groups and Geometries Vol. 28, p. 299-312 (2011),www.santilli-foundation.org/docs/Aringazin-2012.pdf
C. Corda, “An Introduction to Santilli Iso-Numbers, AIP Conf. Proc. Numerical Analysis and Applied Mathematics ICNAAM 2012AIP Conf. Proc. 1479, 1013-1015 (2012); doi: 10.1063/1.4756316, 2012 American Institute of Physics 978-0-7354-1091-6/30.0 (2013), www.santilli-foundation.org/docs/Isonumbers.pdf
J. V. Kadeisvili, “Elements of functional isoanalysis,” Algebras, Groups and Geometries Vol. 9, p. 283-318 (1992).
J. V. Kadeisvili, “Elements of the Fourier-Santilli isotransforms,” Algebras, Groups and Geometries Vol. 9, p. 319-342 (1992).
A. K. Aringazin, D. A. Kirukhin, and R. M. Santilli, “Isotopic Generalization of the Legendre, Jacobi, and Bessel Functions”, Algebras, Groups and Geometries Vol. 12, p. 255-305 (1995).
Gr. T. Tsagas, Algebras, Groups and Geometries Vol. 12, p. 1-65 and p. 67-88 (1995),www.santilli-foundation.org/docs/Santilli-324.pdf
R. M. Falcon Ganfornina and J. Nunez Valdes, “Studies on the Tsagas-Sourlas-Santilli Isotopology,” Algebras, Groups and Geome- tries Vol. 20, p. 1023 (2003)www.santilli-foundation.org/docs/isotopologia.pdf
R. M. Santilli, “Nonlocal-Integral Isotopies of Differential Calculus, Mechanics and Geometries,” in Isotopies of Contemporary Mathemat- ical Structures,” Rendiconti Circolo Matematico Palermo, Suppl. Vol. 42, p. 7-82 (1996),www.santilli-foundation.org/docs/Santilli-37.pdf
R. M. Santilli, “Lie-isotopic Lifting of Special Relativity for Extended Deformable Particles,” Lettere Nuovo Cimento Vol. 37, p. 545-551 (1983),www.santilli-foundation.org/docs/Santilli-50.pdf
A. S. Muktibodh and R. M. Santilli, “Studies of the Regular and Irregular Isorepresentations of the Lie-Santilli Isotheory,” Journal of Generalized Lie Theories Vol. 11, p. 1-7 (2017),www.santilli-foundation.org/docs/isorep-Lie-Santilli-2017.pdf
J. V. Kadeisvili, ’“An introduction to the Lie-Santilli isotopic theory,” Mathematical Methods in Applied Sciences Vol. 19, p. 1341372 (1996), available on the website,www.santilli-foundation.org/docs/Santilli-30.pdf
T. Vougiouklis, “Hypermathematics, Hv-Structures, Hypernumbers, Hypermatrices and Lie-Santilli Admissibility,” American Journal of Modern Physics, Vol. 4, p. 38-46 (2018), also appeared in Foundations of Hadronic Mathematics Dedicated to the 80th Birthday of Prof. R. M. Santilli,www.santilli-foundation.org/docs/10.11648.j.ajmp.s.2015040501.15.pdf
R. M. Santilli, “Invariant Lie-isotopic and Lie-admissible formulation of quantum deformations,” Found. Phys. Vol. 27, p. 1159-1177 (1997), www.santilli-foundation.org/docs/Santilli-06.pdf
A. O. E. Animalu and R. M. Santilli, in Hadronic Mechanics and Non- potential Interactions, M. Mijatovic, Editor, Nova Science, New York, p. 19-22 (l990).
H. C. Myung and R. M. Santilli, “Modular-isotopic Hilbert space formulation of the exterior strong problem,” Hadronic Journal Vol. 5, p. 1277-1366 (1982), www.santilli-foundation.org/docs/Santilli-201.pdf
R. M. Santilli, “Relativistic hadronic mechanics: nonunitary, axiom- preserving completion of relativistic quantum mechanics,” Found. Phys. Vol. 27, p. 625-655 (1997), www.santilli-foundation.org/docs/Santilli-15.pdf
R. M. Santilli, “Recent theoretical and experimental evidence on the synthesis of the neutron,” Communication of the JINR, Dubna, Rus- sia, No. E4-93-252 (1993), published in the Chinese J. System Eng. and Electr. Vol. 6, p. 177-194 (1995), www.santilli-foundation.org/docs/Santilli-18.pdf
M. Nishioka, “Extenuation of the Dirac-Myung-Santilli isodelta functions to field theory,” Lettere Nuovo Cimento Vol. 39, p. 369-372 (1984), www.santilli-foundation.org/docs/Santilli-202.pdf
M. Nishioka, “An introduction to gauge fields by the Lie-isotopic lifting of the Hilbert space,” Lettere Nuovo Cimento Vol. 40, p. 309-312 (1984).
M. Nishioka, “Extension of the Dirac-Myung-Santilli delta function to field theory,” Lettere Nuovo Cimento Vol. 39, p. 369-372 (1984).
M. Nishioka, “Remarks on the Lie algebras appearing in the Lie- isotopic lifting of gauge theories,” Nuovo Cimento Vol. 85 p. 331-336 (1985).
R. Mignani, Lettere Nuovo Cimento Vol. 39, p. 406-410 (1984).
R. Mignani, Lettere Nuovo Cimento Vol. 43, p. 355-369 (1985).
R. Mignani, Hadronic Journal Vol. 9, p. 103133 (1986).
A. K. Aringazin, D. A. Kirukhin, and R. M. Santilli,“Nonpotential elastic scattering of spinning particles,” Hadronic J. Vol. 18, p. 257-271 (1995),www.santilli-foundation.org/docs/Santilli-502.pdf
A. O. E. Animalu and R. M. Santilli, “Nonunitary Lie-isotopic and Lie-admissible scattering theories of hadronic mechanics,” in the Pro- ceedings of the Third International Conference on the Lie-Admissible Treatment of Irreversible Processes, C. Corda, Editor, Kathmandu University, papers I to V, p. 165 on (2011):www.santilli-foundation.org/docs/Isoscattering-I.pdf www.santilli-foundation.org/docs/Isoscattering-II.pdf www.santilli-foundation.org/docs/Isoscattering-III.pdf www.santilli-foundation.org/docs/Isoscattering-IV.pdf www.santilli-foundation.org/docs/Isoscattering-V.pdf
B. Davies, “Non-unitary scattering theory and capture, I: Hilbert space theory,” Comm. Math. Phys. Vol. 71, p. 14721367 (190).
DOI: http://dx.doi.org/10.23755/rm.v38i0.516
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