Deformations of the Canonical Commutation Relations and Metric Structures
Using Connes distance formula in noncommutative geometry, it is possible to retrieve the Euclidean distance from the canonical commutation relations of quantum mechanics. In this note, we study modifications of the distance induced by a deformation of the position-momentum commutation relations. We...
Збережено в:
| Дата: | 2014 |
|---|---|
| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2014
|
| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/146655 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Deformations of the Canonical Commutation Relations and Metric Structures / F. D'Andrea, F. Lizzi, P. Martinetti // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 33 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-146655 |
|---|---|
| record_format |
dspace |
| spelling |
irk-123456789-1466552019-02-11T01:24:47Z Deformations of the Canonical Commutation Relations and Metric Structures D'Andrea, F. Lizzi, F. Martinetti, P. Using Connes distance formula in noncommutative geometry, it is possible to retrieve the Euclidean distance from the canonical commutation relations of quantum mechanics. In this note, we study modifications of the distance induced by a deformation of the position-momentum commutation relations. We first consider the deformation coming from a cut-off in momentum space, then the one obtained by replacing the usual derivative on the real line with the h- and q-derivatives, respectively. In these various examples, some points turn out to be at infinite distance. We then show (on both the real line and the circle) how to approximate points by extended distributions that remain at finite distance. On the circle, this provides an explicit example of computation of the Wasserstein distance. 2014 Article Deformations of the Canonical Commutation Relations and Metric Structures / F. D'Andrea, F. Lizzi, P. Martinetti // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 33 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 58B34; 46L87 DOI:10.3842/SIGMA.2014.062 http://dspace.nbuv.gov.ua/handle/123456789/146655 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
Using Connes distance formula in noncommutative geometry, it is possible to retrieve the Euclidean distance from the canonical commutation relations of quantum mechanics. In this note, we study modifications of the distance induced by a deformation of the position-momentum commutation relations. We first consider the deformation coming from a cut-off in momentum space, then the one obtained by replacing the usual derivative on the real line with the h- and q-derivatives, respectively. In these various examples, some points turn out to be at infinite distance. We then show (on both the real line and the circle) how to approximate points by extended distributions that remain at finite distance. On the circle, this provides an explicit example of computation of the Wasserstein distance. |
| format |
Article |
| author |
D'Andrea, F. Lizzi, F. Martinetti, P. |
| spellingShingle |
D'Andrea, F. Lizzi, F. Martinetti, P. Deformations of the Canonical Commutation Relations and Metric Structures Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
D'Andrea, F. Lizzi, F. Martinetti, P. |
| author_sort |
D'Andrea, F. |
| title |
Deformations of the Canonical Commutation Relations and Metric Structures |
| title_short |
Deformations of the Canonical Commutation Relations and Metric Structures |
| title_full |
Deformations of the Canonical Commutation Relations and Metric Structures |
| title_fullStr |
Deformations of the Canonical Commutation Relations and Metric Structures |
| title_full_unstemmed |
Deformations of the Canonical Commutation Relations and Metric Structures |
| title_sort |
deformations of the canonical commutation relations and metric structures |
| publisher |
Інститут математики НАН України |
| publishDate |
2014 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/146655 |
| citation_txt |
Deformations of the Canonical Commutation Relations and Metric Structures / F. D'Andrea, F. Lizzi, P. Martinetti // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 33 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT dandreaf deformationsofthecanonicalcommutationrelationsandmetricstructures AT lizzif deformationsofthecanonicalcommutationrelationsandmetricstructures AT martinettip deformationsofthecanonicalcommutationrelationsandmetricstructures |
| first_indexed |
2023-05-20T17:25:21Z |
| last_indexed |
2023-05-20T17:25:21Z |
| _version_ |
1796153258728751104 |