Exponential Formulas, Normal Ordering and the Weyl-Heisenberg Algebra
We consider a class of exponentials in the Weyl-Heisenberg algebra with exponents of type at most linear in coordinates and arbitrary functions of momenta. They are expressed in terms of normal ordering, where coordinates stand to the left of momenta. Exponents appearing in normal ordered form satis...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Datum: | 2021 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2021
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/211443 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Exponential Formulas, Normal Ordering and the Weyl-Heisenberg Algebra. Stjepan Meljanac and Rina Štrajn. SIGMA 17 (2021), 084, 7 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862641550232649728 |
|---|---|
| author | Meljanac, Stjepan Rina Štrajn |
| author_facet | Meljanac, Stjepan Rina Štrajn |
| citation_txt | Exponential Formulas, Normal Ordering and the Weyl-Heisenberg Algebra. Stjepan Meljanac and Rina Štrajn. SIGMA 17 (2021), 084, 7 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We consider a class of exponentials in the Weyl-Heisenberg algebra with exponents of type at most linear in coordinates and arbitrary functions of momenta. They are expressed in terms of normal ordering, where coordinates stand to the left of momenta. Exponents appearing in normal ordered form satisfy differential equations with boundary conditions that could be solved perturbatively order by order. Two propositions are presented for the Weyl-Heisenberg algebra in 2 dimensions and their generalizations in higher dimensions. These results can be applied to arbitrary noncommutative spaces for the construction of star products, coproducts of momenta, and twist operators. They can also be related to the BCH formula.
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| first_indexed | 2026-03-15T06:42:32Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211443 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-15T06:42:32Z |
| publishDate | 2021 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Meljanac, Stjepan Rina Štrajn 2026-01-02T08:35:06Z 2021 Exponential Formulas, Normal Ordering and the Weyl-Heisenberg Algebra. Stjepan Meljanac and Rina Štrajn. SIGMA 17 (2021), 084, 7 pages 1815-0659 2020 Mathematics Subject Classification: 16S32; 81R60 arXiv:2105.12593 https://nasplib.isofts.kiev.ua/handle/123456789/211443 https://doi.org/10.3842/SIGMA.2021.084 We consider a class of exponentials in the Weyl-Heisenberg algebra with exponents of type at most linear in coordinates and arbitrary functions of momenta. They are expressed in terms of normal ordering, where coordinates stand to the left of momenta. Exponents appearing in normal ordered form satisfy differential equations with boundary conditions that could be solved perturbatively order by order. Two propositions are presented for the Weyl-Heisenberg algebra in 2 dimensions and their generalizations in higher dimensions. These results can be applied to arbitrary noncommutative spaces for the construction of star products, coproducts of momenta, and twist operators. They can also be related to the BCH formula. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Exponential Formulas, Normal Ordering and the Weyl-Heisenberg Algebra Article published earlier |
| spellingShingle | Exponential Formulas, Normal Ordering and the Weyl-Heisenberg Algebra Meljanac, Stjepan Rina Štrajn |
| title | Exponential Formulas, Normal Ordering and the Weyl-Heisenberg Algebra |
| title_full | Exponential Formulas, Normal Ordering and the Weyl-Heisenberg Algebra |
| title_fullStr | Exponential Formulas, Normal Ordering and the Weyl-Heisenberg Algebra |
| title_full_unstemmed | Exponential Formulas, Normal Ordering and the Weyl-Heisenberg Algebra |
| title_short | Exponential Formulas, Normal Ordering and the Weyl-Heisenberg Algebra |
| title_sort | exponential formulas, normal ordering and the weyl-heisenberg algebra |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211443 |
| work_keys_str_mv | AT meljanacstjepan exponentialformulasnormalorderingandtheweylheisenbergalgebra AT rinastrajn exponentialformulasnormalorderingandtheweylheisenbergalgebra |