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Group Momentum Space and Hopf Algebra Symmetries of Point Particles Coupled to 2+1 Gravity

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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Main Authors: Arzano, M., Latini, D., Lotito, M.
Format: Article
Language:English
Published: Інститут математики НАН України 2014
Series:Symmetry, Integrability and Geometry: Methods and Applications
Online Access:http://dspace.nbuv.gov.ua/handle/123456789/146603
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spelling 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
work_keys_str_mv AT arzanom groupmomentumspaceandhopfalgebrasymmetriesofpointparticlescoupledto21gravity
AT latinid groupmomentumspaceandhopfalgebrasymmetriesofpointparticlescoupledto21gravity
AT lotitom groupmomentumspaceandhopfalgebrasymmetriesofpointparticlescoupledto21gravity
first_indexed 2023-05-20T17:25:11Z
last_indexed 2023-05-20T17:25:11Z
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