Isotopic lifting of analytic and quantum mechanics
In a preceding article we have introduced the isotopies of the differential calculus and of Newton's equations of motion. In this second paper we use these results lo construct the isotopies of analytic and quantum mechanics. We show that the isotopies of Hamiltonian mechanics permit the deriva...
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| Format: | Article |
| Language: | English |
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Universidad del Zulia
2011-01-01
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| Series: | Revista Técnica de la Facultad de Ingeniería |
| Subjects: | |
| Online Access: | https://www.produccioncientificaluz.org/index.php/tecnica/article/view/5492 |
| _version_ | 1811296876851363840 |
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| author | Ruggero María Santilli |
| author_facet | Ruggero María Santilli |
| author_sort | Ruggero María Santilli |
| collection | DOAJ |
| description | In a preceding article we have introduced the isotopies of the differential calculus and of Newton's equations of motion. In this second paper we use these results lo construct the isotopies of analytic and quantum mechanics. We show that the isotopies of Hamiltonian mechanics permit the derivation from a first-order isovariational principie of the most general possiblenonlinear integro-differential Newton's equations by providing in particular a representation of the extended and deformable shape of the body considered as well as of nonlocal-integral and variationally non-self-adjoint forces. We then identify the isotopies of conventional quantization and show that they lead lo unique and unambiguous isotopies of quantum mechanics capable of preserving all the essential characteristics of the original isotopic Newton's equations, thus permitting the representation in the fixed inertial frame of the experimenter of nonlinear, nonlocal and nonhamiltonian systems, with considerable broadening of the arena of applicability of conventional formulations.
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| first_indexed | 2024-04-13T05:56:05Z |
| format | Article |
| id | doaj.art-879309d3d84543deb1afb3f0fb305477 |
| institution | Directory Open Access Journal |
| issn | 0254-0770 2477-9377 |
| language | English |
| last_indexed | 2024-04-13T05:56:05Z |
| publishDate | 2011-01-01 |
| publisher | Universidad del Zulia |
| record_format | Article |
| series | Revista Técnica de la Facultad de Ingeniería |
| spelling | doaj.art-879309d3d84543deb1afb3f0fb3054772022-12-22T02:59:38ZengUniversidad del ZuliaRevista Técnica de la Facultad de Ingeniería0254-07702477-93772011-01-01191Isotopic lifting of analytic and quantum mechanicsRuggero María Santilli0lstituto per la Ricerca di Base Castello Pignatelli-ItaliaIn a preceding article we have introduced the isotopies of the differential calculus and of Newton's equations of motion. In this second paper we use these results lo construct the isotopies of analytic and quantum mechanics. We show that the isotopies of Hamiltonian mechanics permit the derivation from a first-order isovariational principie of the most general possiblenonlinear integro-differential Newton's equations by providing in particular a representation of the extended and deformable shape of the body considered as well as of nonlocal-integral and variationally non-self-adjoint forces. We then identify the isotopies of conventional quantization and show that they lead lo unique and unambiguous isotopies of quantum mechanics capable of preserving all the essential characteristics of the original isotopic Newton's equations, thus permitting the representation in the fixed inertial frame of the experimenter of nonlinear, nonlocal and nonhamiltonian systems, with considerable broadening of the arena of applicability of conventional formulations. https://www.produccioncientificaluz.org/index.php/tecnica/article/view/5492isotopiesisolagrangian and isohamiltonian mechanicshadronic mechanics |
| spellingShingle | Ruggero María Santilli Isotopic lifting of analytic and quantum mechanics Revista Técnica de la Facultad de Ingeniería isotopies isolagrangian and isohamiltonian mechanics hadronic mechanics |
| title | Isotopic lifting of analytic and quantum mechanics |
| title_full | Isotopic lifting of analytic and quantum mechanics |
| title_fullStr | Isotopic lifting of analytic and quantum mechanics |
| title_full_unstemmed | Isotopic lifting of analytic and quantum mechanics |
| title_short | Isotopic lifting of analytic and quantum mechanics |
| title_sort | isotopic lifting of analytic and quantum mechanics |
| topic | isotopies isolagrangian and isohamiltonian mechanics hadronic mechanics |
| url | https://www.produccioncientificaluz.org/index.php/tecnica/article/view/5492 |
| work_keys_str_mv | AT ruggeromariasantilli isotopicliftingofanalyticandquantummechanics |