In this paper, we outline the various branches of hadronic mathematics and their applications to corresponding branches of hadronic mechanics and chemistry as conceived by the Italian-American scientist Ruggero Maria Santilli. According to said conception, hadronic mathematics comprises the following branches for the treatment of matter in conditions of increasing complexity: 1) 20th century mathematics based on Lie’s theory; 2) Iso Mathematics based on Santilli’s isotopies of Lie’s theory; 3) Geno Mathematics based on Santilli’s formulation of Albert’s Lie-admissibility; 4) Hyper Mathematics based on a multi-valued realization of genomathematics with classical operations; and 5) Hyper Mathematics based on Vougiouklis Hv hyperstructures expressed in terms of hyperoperations. Additionally, hadronic mathematics comprises the anti-Hermitean images (called isoduals) of the five preceding mathematics for the description of antimatter also in conditions of increasing complexity. The outline presented in this paper includes the identification of represented physical or chemical systems, the main mathematical structure, and the main dynamical equations per each branch. We also show the axiomatic consistency of various branches of hadronic mathematics as sequential coverings of 20th century mathematics; and indicate a number of open mathematical problems. Novel physical and chemical applications permitted by hadronic mathematics are presented in subsequent collections.
DOI | 10.11648/j.ajmp.s.2017060401.11 |
Published in |
American Journal of Modern Physics (Volume 6, Issue 4-1, August 2017)
This article belongs to the Special Issue Issue III: Foundations of Hadronic Chemistry |
Page(s) | 1-16 |
Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
Copyright |
Copyright © The Author(s), 2024. Published by Science Publishing Group |
Santilli Isomathematics, Genomathematics, Hypermathematics
[1] | R. M. Santilli, Foundations of Theoretical Mechanics, Volumes I (1978) and II (1982) Springer-Verlag, Heidelberg, Germany (1983). http://www.santilli-foundation.org/docs/Santilli-209.pdf, http://www.santilli-foundation.org/docs/santilli-69.pdf |
[2] | R. M. Santilli, Isonumbers and genonumbers of dimension 1, 2, 4, 8, their isoduals and pseudoisoduals, and "hidden numbers" of dimension 3, 5, 6, 7, Algebras, Groups and Geometries (1993), 273-322. http://www.santilli-foundation.org/docs/Santilli-34.pdf |
[3] | R. M. Santilli, Nonlocal-integral isotopies of differential calculus, geometries and mechanics, Rendiconti Circolo Matematico di Palermo, Supplemento, in press, 1996, http://www.santilli-foundation.org/docs/Santilli-37.pdf |
[4] | R. M. Santilli, Elements of Hadronic Mechanics, Vol. I (1995), Vol. II 91995), Academy of Sciences, Kiev, http://www.santilli-foundation.org/docs/Santilli-300.pdf, http://www.santilli-foundation.org/docs/Santilli-301.pdf |
[5] | R. M. Santilli, Hadronic Mathematics, Mechanics and Chemistry, Volumes I, II, III, IV and V, International Academic Press (2008), http://www.i-b-r.org/Hadronic-Mechanics.htm |
[6] | H. C. Myung and R. M. Santilli, "Modular-isotopic Hilbert space formulation of the exterior strong problem," Hadronic Journal, 1277-1366 (1982), http://www.santilli-foundation.org/docs/Santilli-201.pdf. |
[7] | D. S. Sourlas and G. T. Tsagas, Mathematical Foundation of the Lie-Santilli Theory, Ukraine Academy of Sciences 91993), available as free download from http://www.santilli-foundation.org/docs/santilli-70.pdf |
[8] | J. V. Kadeisvili, Santilli’s Isotopies of Contemporary Algebras, Geometries and Relativities, Ukraine Academy of Sciences, Second edition (1997), available as free download from http://www.santilli-foundation.org/docs/Santilli-60.pdf |
[9] | Chun-Xuan Jiang, Foundations of Santilli Isonumber Theory, International Academic Press (2001), http://www.i-b-r.org/docs/jiang.pdf |
[10] | Raul M. Falcon Ganfornina and Juan Nunez Valdes, Fundamentos de la Isdotopia de Santilli, International Academic Press (2001), http://www.i-b-r.org/docs/spanish.pdf, English translations Algebras, Groups and Geometries Vol. 32, pages 135-308 (2015), http://www.i-b-r.org/docs/Aversa-translation.pdf |
[11] | Raul M. Falcon Ganfornina and Juan Nunez Valdes, “Studies on the Tsagas-Sourlas-Santilli Isotopology,” Algebras, Groups and Geometries Vol. 20, 1 (2003), http://www.santilli-foundation.org/docs/isotopologia.pdf |
[12] | S. Georgiev, Foundations of the IsoDifferential Calculus, Volumes, I, II, III, IV and V, Nova Scientific Publisher (2015 on). |
[13] | A. S. Muktibodh, "Iso-Galois Fields," Hadronic Journal, 13-29 (2015), http://www.santilli-foundation.org/docs/Iso-Galoisfields.pdf |
[14] | 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), available in free pdf download from the link, http://www.santilli-foundation.org/santilli-scientific-discoveries.html |
[15] | R. M. Santilli, Embedding of Lie algebras in Lie-admissible algebras. Nuovo Cimento, 570 (1967), http://www.santilli-foundation.org/docs/Santilli-54.pdf |
[16] | A. A. Albert, Trans. Amer. Math. Soc., 552 (1948). |
[17] | R. M. Santilli, “An introduction to Lie-admissible algebras,” Suppl. Nuovo Cimento, 1225 (1968). |
[18] | R. M. Santilli, “Dissipativity and Lie-admissible algebras,” Meccanica, 3 (1969). |
[19] | P. Roman and R. M. Santilli, "A Lie-admissible model for dissipative plasma," Lettere Nuovo Cimento Vol. 2, 449-455 (1969). |
[20] | R. M. Santilli, On a possible Lie-admissible covering of the Galilei relativity in Newtonian mechanics for nonconservative and Galilei non-invariant systems, Hadronic J [1978], 223-423; Addendum, ibid. 1 (1978), 1279-1342. http://www.santilli-foundation.org/docs/Santilli-58.pdf |
[21] | R. M. Santilli, Lie-admissible Approach to the Hadronic Structure, Volumes I (1978) and II (1981), Hadronic Press (1981), http://www.santilli-foundation.org/docs/santilli-71.pdf, http://www.santilli-foundation.org/docs/santilli-72.pdf |
[22] | R. M. Santilli, "Invariant Lie-admissible formulation of quantum deformations," Found. Phys., 1159- 1177 (1997), http://www.santilli-foundation.org/docs/Santilli-06.pdf |
[23] | R. M. Santilli, “Lie-admissible invariant representation of irreversibility for matter and antimatter at the classical and operator levels,” Nuovo Cimento B bf 121, 443 (2006), http://www.santilli-foundation.org/docs/Lie-admiss-NCB-I.pdf |
[24] | A. Schoeber, Editor, Irreversibility and Non-potentiality in Statistical Mechanics, Hadronic Press (1984), http://www.santilli-foundation.org/docs/Santilli-110.pdf |
[25] | C. Corda, Editor, Proceedings of the Third International Conference on the Lie-Admissible Treatment of Irreversible Processes, Kathmandu University (2011), http://www.santilli-foundation.org/docs/Nepal-2011.pdf |
[26] | M. Tomber, Bibliography and Index in non-Associative Algebras, Volumes I, II, III, Hadronic Press (1986), http://www.santilli-foundation.org/docs/Tomber.pdf |
[27] | C. R. Illert and R. M. Santilli, Foundations of Theoretical Conciology, Hadronic Press (1995), http://www.santilli-foundation.org/docs/santilli-109.pdf |
[28] | R. M. Santilli, Isotopic, Genotopic and Hyperstructural Methods in Theoretical Biology, Ukraine Academy of Sciences, Kiev (1994), http://www.santilli-foundation.org/docs/santilli-67.pdf |
[29] | T. Vougiouklis, "The Santilli theory ’invasion’ in hyperstructures," Algebras, Groups and Geometries Vol. 28, pages 83-104 (2011), http://www.santilli-foundation.org/docs/santilli-invasion.pdf |
[30] | Pipina Nikolaidou, Thomas Vougiouklis, "The Lie-Santilli admissible hyperalgebras of type A_n," Ratio Matematica Vol. 26, pages 113128 (2014), American Journal of Modern Physics Vol. 4, pages 5-9 (2015), http://www.santilli-foundation.org/docs/115-RM-2677.pdf |
[31] | T. Vougiouklis, "On the Iso-H_{v} numbers," in press, http://www.santilli-foundation.org/docs/isoHv-numbers.pdf |
[32] | R. M. Santilli, “Representation of antiparticles via isodual numbers, spaces and geometries,” Comm. Theor. Phys. vol. 3, 1994, pp. 153-181, http://www.santillifoundation.org/docs/Santilli-112.pdf |
[33] | R. M. Santilli, “Does antimatter emit a new light?” Invited paper for the proceedings of the International Conference on Antimatter, held in Sepino, Italy, on May 1996, invited publication in Hyperfine Interactions vol. 109, 1997, pp. 63-81, http://www.santilli-foundation.org/docs/Santilli-28.pdf |
[34] | R. M. Santilli and T. Vougiouklis, "Lie-admissible hyperalgebras," Italian Journal of Pure and Applied mathematics Vol. 31, pages 239-254 (2013), http://www.santilli-foundation.org/docs/111 santilli-vougiouklis.pdf |
[35] | B. Davvaz, Hyperings Theory and Applications, International Academic Press (2007), http://www.santilli-foundation.org/docs/Davvaz.pdf |
[36] | R. M. Santilli, “Representation of antiparticles via isodual numbers, spaces and geometries,” Comm. Theor. Phys. vol. 3, 1994, pp. 153-181, http://www.santillifoundation.org/docs/Santilli-112.pdf |
[37] | Santilli, R. M. “Classical isodual theory of antimatter and its prediction of antigravity,” Intern. J. Modern Phys. 1999, A 14, 2205-2238, http://www.santilli-foundation.org/docs/Santilli-09.pdf |
[38] | R. M. Santilli, ÒDoes antimatter emit a new light?Ó Invited paper for the proceedings of the International Conference on Antimatter, held in Sepino, Italy, on May 1996, invited publication in Hyperfine Interactions vol. 109, 1997, pp. 63-81, http://www.santilli-foundation.org/docs/Santilli-28.pdf |
[39] | Santilli, R. M. “Isominkowskian Geometry for the Gravitational Treatment of Matter and its Isodual for Antimatter,” Intern. J. Modern Phys. 1998, D 7, 351, http://www.santilli-foundation.org/docs/Santilli-35.pdfR. |
[40] | R. M. Santilli, Isodual Theory of Antimatter with Applications to Antigravity, Grand Unifications and Cosmology, Springer (2006). |
[41] | R. M. Santilli, "Apparent detection of antimatter galaxies via a telescope with convex lenses," Clifford Analysis, Clifford Algebras and their Applications vol. 3, 2014, pages 1-26 (Cambridge, UK), http://www.santilli-foundation.org/docs/Antimatter-telescope-2013-final.pdf |
[42] | P. Bhujbal, J. V. Kadeisvili, A. Nas, S Randall, and T. R. Shelke, “Preliminary confirmation of antimatter detection via Santilli telescope with concave lenses,” Clifford Analysis, Clifford Algebras and their Applications Vol. 3, pages 27-39, 2014 (Cambridge, UK), www.santilli-foundation.org/docs/Con-Ant-Tel-2013.pdf |
[43] | S. Beghella-Bartoli, Prashant M. Bhujbal, Alex Nas, “Confirmation of antimatter detection via Santilli telescope with concave lenses,” American Journal of Modern Physics Vol. 4, pages 34-41 (2015), http://www.santilli-foundation.org/docs/antimatter-detect-2014.pdf |
[44] | B. Davvaz, R. M. Santilli and T. Vougiouklis, Studies Of Multi-Valued Hyperstructures For The characterization Of Matter-Antimatter Systems And Their Extension Proceedings of the Third International Conference on the Lie-Admissible Treatment of Irreversible Processes, C. Corda, Editor, Kathmandu University (2011), pages 45-57, http://www.santilli-foundation.org/docs/Davvaz-Sant-Vou.pdf |
[45] | Scientific archives from 1967 to 2007, http://www.santilli-foundation.org/docs/Santilli-64.pdf, Scientific Archives from 2007 to 2015, http://www.santilli-foundation.org/news.html |
APA Style
Richard Anderson. (2017). Outline of Hadronic Mathematics, Mechanics and Chemistry as Conceived by R. M. Santilli. American Journal of Modern Physics, 6(4-1), 1-16. https://doi.org/10.11648/j.ajmp.s.2017060401.11
ACS Style
Richard Anderson. Outline of Hadronic Mathematics, Mechanics and Chemistry as Conceived by R. M. Santilli. Am. J. Mod. Phys. 2017, 6(4-1), 1-16. doi: 10.11648/j.ajmp.s.2017060401.11
@article{10.11648/j.ajmp.s.2017060401.11, author = {Richard Anderson}, title = {Outline of Hadronic Mathematics, Mechanics and Chemistry as Conceived by R. M. Santilli}, journal = {American Journal of Modern Physics}, volume = {6}, number = {4-1}, pages = {1-16}, doi = {10.11648/j.ajmp.s.2017060401.11}, url = {https://doi.org/10.11648/j.ajmp.s.2017060401.11}, eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmp.s.2017060401.11}, abstract = {In this paper, we outline the various branches of hadronic mathematics and their applications to corresponding branches of hadronic mechanics and chemistry as conceived by the Italian-American scientist Ruggero Maria Santilli. According to said conception, hadronic mathematics comprises the following branches for the treatment of matter in conditions of increasing complexity: 1) 20th century mathematics based on Lie’s theory; 2) Iso Mathematics based on Santilli’s isotopies of Lie’s theory; 3) Geno Mathematics based on Santilli’s formulation of Albert’s Lie-admissibility; 4) Hyper Mathematics based on a multi-valued realization of genomathematics with classical operations; and 5) Hyper Mathematics based on Vougiouklis Hv hyperstructures expressed in terms of hyperoperations. Additionally, hadronic mathematics comprises the anti-Hermitean images (called isoduals) of the five preceding mathematics for the description of antimatter also in conditions of increasing complexity. The outline presented in this paper includes the identification of represented physical or chemical systems, the main mathematical structure, and the main dynamical equations per each branch. We also show the axiomatic consistency of various branches of hadronic mathematics as sequential coverings of 20th century mathematics; and indicate a number of open mathematical problems. Novel physical and chemical applications permitted by hadronic mathematics are presented in subsequent collections.}, year = {2017} }
TY - JOUR T1 - Outline of Hadronic Mathematics, Mechanics and Chemistry as Conceived by R. M. Santilli AU - Richard Anderson Y1 - 2017/09/26 PY - 2017 N1 - https://doi.org/10.11648/j.ajmp.s.2017060401.11 DO - 10.11648/j.ajmp.s.2017060401.11 T2 - American Journal of Modern Physics JF - American Journal of Modern Physics JO - American Journal of Modern Physics SP - 1 EP - 16 PB - Science Publishing Group SN - 2326-8891 UR - https://doi.org/10.11648/j.ajmp.s.2017060401.11 AB - In this paper, we outline the various branches of hadronic mathematics and their applications to corresponding branches of hadronic mechanics and chemistry as conceived by the Italian-American scientist Ruggero Maria Santilli. According to said conception, hadronic mathematics comprises the following branches for the treatment of matter in conditions of increasing complexity: 1) 20th century mathematics based on Lie’s theory; 2) Iso Mathematics based on Santilli’s isotopies of Lie’s theory; 3) Geno Mathematics based on Santilli’s formulation of Albert’s Lie-admissibility; 4) Hyper Mathematics based on a multi-valued realization of genomathematics with classical operations; and 5) Hyper Mathematics based on Vougiouklis Hv hyperstructures expressed in terms of hyperoperations. Additionally, hadronic mathematics comprises the anti-Hermitean images (called isoduals) of the five preceding mathematics for the description of antimatter also in conditions of increasing complexity. The outline presented in this paper includes the identification of represented physical or chemical systems, the main mathematical structure, and the main dynamical equations per each branch. We also show the axiomatic consistency of various branches of hadronic mathematics as sequential coverings of 20th century mathematics; and indicate a number of open mathematical problems. Novel physical and chemical applications permitted by hadronic mathematics are presented in subsequent collections. VL - 6 IS - 4-1 ER -