From Fractional Quantum Mechanics to Quantum Cosmology: An Overture
Fractional calculus is a couple of centuries old, but its development has been less embraced and it was only within the last century that a program of applications for physics started. Regarding quantum physics, it has been only in the previous decade or so that the corresponding literature resulted...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-03-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/3/313 |
| _version_ | 1828312039588626432 |
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| author | Paulo Vargas Moniz Shahram Jalalzadeh |
| author_facet | Paulo Vargas Moniz Shahram Jalalzadeh |
| author_sort | Paulo Vargas Moniz |
| collection | DOAJ |
| description | Fractional calculus is a couple of centuries old, but its development has been less embraced and it was only within the last century that a program of applications for physics started. Regarding quantum physics, it has been only in the previous decade or so that the corresponding literature resulted in a set of defying papers. In such a context, this manuscript constitutes a cordial invitation, whose purpose is simply to suggest, mostly through a heuristic and unpretentious presentation, the extension of fractional quantum mechanics to cosmological settings. Being more specific, we start by outlining a historical summary of fractional calculus. Then, following this motivation, a (very) brief appraisal of fractional quantum mechanics is presented, but where details (namely those of a mathematical nature) are left for literature perusing. Subsequently, the application of fractional calculus in quantum cosmology is introduced, advocating it as worthy to consider: if the progress of fractional calculus serves as argument, indeed useful consequences will also be drawn (to cite from Leibnitz). In particular, we discuss different difficulties that may affect the operational framework to employ, namely the issues of minisuperspace covariance and fractional derivatives, for instance. An example of investigation is provided by means of a very simple model. Concretely, we restrict ourselves to speculate that with minimal fractional calculus elements, we may have a peculiar tool to inspect the flatness problem of standard cosmology. In summary, the subject of fractional quantum cosmology is herewith proposed, merely realised in terms of an open program constituted by several challenges. |
| first_indexed | 2024-04-13T16:09:23Z |
| format | Article |
| id | doaj.art-ea85741a71d6473b96e18dfec43c36ec |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-04-13T16:09:23Z |
| publishDate | 2020-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-ea85741a71d6473b96e18dfec43c36ec2022-12-22T02:40:18ZengMDPI AGMathematics2227-73902020-03-018331310.3390/math8030313math8030313From Fractional Quantum Mechanics to Quantum Cosmology: An OverturePaulo Vargas Moniz0Shahram Jalalzadeh1Departamento de Física and Centro de Matemática e Aplicações (CMA - UBI), Universidade da Beira Interior, Rua Marquês d’Ávila e Bolama, 6200 Covilhã, PortugalDepartmento de Física, Universidade Federal de Pernambuco, Pernambuco, PE, 52171-900, BrazilFractional calculus is a couple of centuries old, but its development has been less embraced and it was only within the last century that a program of applications for physics started. Regarding quantum physics, it has been only in the previous decade or so that the corresponding literature resulted in a set of defying papers. In such a context, this manuscript constitutes a cordial invitation, whose purpose is simply to suggest, mostly through a heuristic and unpretentious presentation, the extension of fractional quantum mechanics to cosmological settings. Being more specific, we start by outlining a historical summary of fractional calculus. Then, following this motivation, a (very) brief appraisal of fractional quantum mechanics is presented, but where details (namely those of a mathematical nature) are left for literature perusing. Subsequently, the application of fractional calculus in quantum cosmology is introduced, advocating it as worthy to consider: if the progress of fractional calculus serves as argument, indeed useful consequences will also be drawn (to cite from Leibnitz). In particular, we discuss different difficulties that may affect the operational framework to employ, namely the issues of minisuperspace covariance and fractional derivatives, for instance. An example of investigation is provided by means of a very simple model. Concretely, we restrict ourselves to speculate that with minimal fractional calculus elements, we may have a peculiar tool to inspect the flatness problem of standard cosmology. In summary, the subject of fractional quantum cosmology is herewith proposed, merely realised in terms of an open program constituted by several challenges.https://www.mdpi.com/2227-7390/8/3/313quantum cosmologyfractional calculusearly universe |
| spellingShingle | Paulo Vargas Moniz Shahram Jalalzadeh From Fractional Quantum Mechanics to Quantum Cosmology: An Overture Mathematics quantum cosmology fractional calculus early universe |
| title | From Fractional Quantum Mechanics to Quantum Cosmology: An Overture |
| title_full | From Fractional Quantum Mechanics to Quantum Cosmology: An Overture |
| title_fullStr | From Fractional Quantum Mechanics to Quantum Cosmology: An Overture |
| title_full_unstemmed | From Fractional Quantum Mechanics to Quantum Cosmology: An Overture |
| title_short | From Fractional Quantum Mechanics to Quantum Cosmology: An Overture |
| title_sort | from fractional quantum mechanics to quantum cosmology an overture |
| topic | quantum cosmology fractional calculus early universe |
| url | https://www.mdpi.com/2227-7390/8/3/313 |
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