Group Momentum Space and Hopf Algebra Symmetries of Point Particles Coupled to 2+1 Gravity
We present an in-depth investigation of the SL(2,R) momentum space describing point particles coupled to Einstein gravity in three space-time dimensions. We introduce different sets of coordinates on the group manifold and discuss their properties under Lorentz transformations. In particular we show...
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| Дата: | 2014 |
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| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2014
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/146603 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Group Momentum Space and Hopf Algebra Symmetries of Point Particles Coupled to 2+1 Gravity / M. Arzano, D. Latini, M. Lotito // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 33 назв. — англ. |
Репозиторії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1466032019-02-11T01:24:08Z Group Momentum Space and Hopf Algebra Symmetries of Point Particles Coupled to 2+1 Gravity Arzano, M. Latini, D. Lotito, M. We present an in-depth investigation of the SL(2,R) momentum space describing point particles coupled to Einstein gravity in three space-time dimensions. We introduce different sets of coordinates on the group manifold and discuss their properties under Lorentz transformations. In particular we show how a certain set of coordinates exhibits an upper bound on the energy under deformed Lorentz boosts which saturate at the Planck energy. We discuss how this deformed symmetry framework is generally described by a quantum deformation of the Poincaré group: the quantum double of SL(2,R). We then illustrate how the space of functions on the group manifold momentum space has a dual representation on a non-commutative space of coordinates via a (quantum) group Fourier transform. In this context we explore the connection between Weyl maps and different notions of (quantum) group Fourier transform appeared in the literature in the past years and establish relations between them. 2014 Article Group Momentum Space and Hopf Algebra Symmetries of Point Particles Coupled to 2+1 Gravity / M. Arzano, D. Latini, M. Lotito // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 33 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 81R50; 83A05; 83C99 DOI:10.3842/SIGMA.2014.079 http://dspace.nbuv.gov.ua/handle/123456789/146603 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 |
We present an in-depth investigation of the SL(2,R) momentum space describing point particles coupled to Einstein gravity in three space-time dimensions. We introduce different sets of coordinates on the group manifold and discuss their properties under Lorentz transformations. In particular we show how a certain set of coordinates exhibits an upper bound on the energy under deformed Lorentz boosts which saturate at the Planck energy. We discuss how this deformed symmetry framework is generally described by a quantum deformation of the Poincaré group: the quantum double of SL(2,R). We then illustrate how the space of functions on the group manifold momentum space has a dual representation on a non-commutative space of coordinates via a (quantum) group Fourier transform. In this context we explore the connection between Weyl maps and different notions of (quantum) group Fourier transform appeared in the literature in the past years and establish relations between them. |
| format |
Article |
| author |
Arzano, M. Latini, D. Lotito, M. |
| spellingShingle |
Arzano, M. Latini, D. Lotito, M. Group Momentum Space and Hopf Algebra Symmetries of Point Particles Coupled to 2+1 Gravity Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Arzano, M. Latini, D. Lotito, M. |
| author_sort |
Arzano, M. |
| title |
Group Momentum Space and Hopf Algebra Symmetries of Point Particles Coupled to 2+1 Gravity |
| title_short |
Group Momentum Space and Hopf Algebra Symmetries of Point Particles Coupled to 2+1 Gravity |
| title_full |
Group Momentum Space and Hopf Algebra Symmetries of Point Particles Coupled to 2+1 Gravity |
| title_fullStr |
Group Momentum Space and Hopf Algebra Symmetries of Point Particles Coupled to 2+1 Gravity |
| title_full_unstemmed |
Group Momentum Space and Hopf Algebra Symmetries of Point Particles Coupled to 2+1 Gravity |
| title_sort |
group momentum space and hopf algebra symmetries of point particles coupled to 2+1 gravity |
| publisher |
Інститут математики НАН України |
| publishDate |
2014 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/146603 |
| citation_txt |
Group Momentum Space and Hopf Algebra Symmetries of Point Particles Coupled to 2+1 Gravity / M. Arzano, D. Latini, M. Lotito // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 33 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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2023-05-20T17:25:11Z |
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2023-05-20T17:25:11Z |
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