Group Momentum Space and Hopf Algebra Symmetries of Point Particles Coupled to 2+1 Gravity
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Group Momentum Space and Hopf Algebra Symmetries of Point Particles Coupled to 2+1 Gravity
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| Creator |
Arzano, M.
Latini, D. Lotito, M. |
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| 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.
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| Date |
2019-02-10T09:53:00Z
2019-02-10T09:53:00Z 2014 |
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| Type |
Article
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| Identifier |
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 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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