Academic Journal
On the unitary irreducible representations of the D=2 Euclidean and Poincaré groups.
| Τίτλος: | On the unitary irreducible representations of the D=2 Euclidean and Poincaré groups. |
|---|---|
| Συγγραφείς: | Camilletti, G.1 (AUTHOR) giovanni.camilletti@uv.es, Lledó, M. A.1 (AUTHOR) maria.lledo@ific.uv.es, del Olmo, M. A.2 (AUTHOR) marianoantonio.olmo@uva.es |
| Πηγή: | International Journal of Geometric Methods in Modern Physics. Sep2026, p1. 36p. |
| Θεματικοί όροι: | *Representations of groups (Algebra), *Representation theory, *Lie groups, *Symmetry groups, *Hilbert space, *Bessel functions |
| Περίληψη: | In this paper, we present an explicit construction of the unitary irreducible representations of the two-dimensional Euclidean and Poincaré groups, together with their Spin double covers, by means of Mackey’s theory of induced representations for semidirect products. In dimension D = 2, the simplicity of the corresponding little groups allows a complete explicit treatment of momentum orbits, equivariant wavefunctions, and representation operators. For the Euclidean group, the matrix elements of the infinite-dimensional representations are expressed in terms of Bessel functions. For the Poincaré group, the richer Lorentzian orbit structure leads to matrix elements involving modified Bessel and Hankel functions and, in some cases, tempered distributions, requiring the use of Rigged Hilbert Spaces. This work illustrates the interplay among induced representations, harmonic analysis on Lie groups, spin geometry, and special functions in a fully explicit relativistic setting. [ABSTRACT FROM AUTHOR] |
| Βάση Δεδομένων: | Academic Search Index |
| FullText | Text: Availability: 0 |
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| Header | DbId: asx DbLabel: Academic Search Index An: 196846704 RelevancyScore: 1452 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 1452.427734375 |
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| Items | – Name: Title Label: Title Group: Ti Data: On the unitary irreducible representations of the D=2 Euclidean and Poincaré groups. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Camilletti%2C+G%2E%22">Camilletti, G.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> giovanni.camilletti@uv.es</i><br /><searchLink fieldCode="AR" term="%22Lledó%2C+M%2E+A%2E%22">Lledó, M. A.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> maria.lledo@ific.uv.es</i><br /><searchLink fieldCode="AR" term="%22del+Olmo%2C+M%2E+A%2E%22">del Olmo, M. A.</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> marianoantonio.olmo@uva.es</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22International+Journal+of+Geometric+Methods+in+Modern+Physics%22">International Journal of Geometric Methods in Modern Physics</searchLink>. Sep2026, p1. 36p. – Name: Subject Label: Subject Terms Group: Su Data: *<searchLink fieldCode="DE" term="%22Representations+of+groups+%28Algebra%29%22">Representations of groups (Algebra)</searchLink><br />*<searchLink fieldCode="DE" term="%22Representation+theory%22">Representation theory</searchLink><br />*<searchLink fieldCode="DE" term="%22Lie+groups%22">Lie groups</searchLink><br />*<searchLink fieldCode="DE" term="%22Symmetry+groups%22">Symmetry groups</searchLink><br />*<searchLink fieldCode="DE" term="%22Hilbert+space%22">Hilbert space</searchLink><br />*<searchLink fieldCode="DE" term="%22Bessel+functions%22">Bessel functions</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: In this paper, we present an explicit construction of the unitary irreducible representations of the two-dimensional Euclidean and Poincaré groups, together with their Spin double covers, by means of Mackey’s theory of induced representations for semidirect products. In dimension D = 2, the simplicity of the corresponding little groups allows a complete explicit treatment of momentum orbits, equivariant wavefunctions, and representation operators. For the Euclidean group, the matrix elements of the infinite-dimensional representations are expressed in terms of Bessel functions. For the Poincaré group, the richer Lorentzian orbit structure leads to matrix elements involving modified Bessel and Hankel functions and, in some cases, tempered distributions, requiring the use of Rigged Hilbert Spaces. This work illustrates the interplay among induced representations, harmonic analysis on Lie groups, spin geometry, and special functions in a fully explicit relativistic setting. [ABSTRACT FROM AUTHOR] |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1142/s0219887826300035 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 36 StartPage: 1 Subjects: – SubjectFull: Representations of groups (Algebra) Type: general – SubjectFull: Representation theory Type: general – SubjectFull: Lie groups Type: general – SubjectFull: Symmetry groups Type: general – SubjectFull: Hilbert space Type: general – SubjectFull: Bessel functions Type: general Titles: – TitleFull: On the unitary irreducible representations of the D=2 Euclidean and Poincaré groups. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Camilletti, G. – PersonEntity: Name: NameFull: Lledó, M. A. – PersonEntity: Name: NameFull: del Olmo, M. A. IsPartOfRelationships: – BibEntity: Dates: – D: 09 M: 09 Text: Sep2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 02198878 Titles: – TitleFull: International Journal of Geometric Methods in Modern Physics Type: main |
| ResultId | 1 |