Abstract
This paper concerns the problem of reduction of unitary
irreducible representations of the Poincaré group
$\mathrm{P}(1,n)$ with respect to representations of its subgroup
$\mathrm{SO}(1,n)$. Based on a generalization of the Wigner-Eckart
theorem, we obtain matrix elements of the shift operators in the
$\mathrm{SO}(1,n)$-basis.
Робота присвячена проблемі редукції унітарних незвідних
представлень групи Пуанкаре $P(1, n)$ відносно представлень її
підгрупи $SO(1, n)$. На основі узагальнення теореми Вігнера-Еккарта
отримано матричні елементи операторів зсуву в $SO(1, n)$-базисі.
Key words: Poincaré group, irreducible representation, unitary
representation, decomposition.
Full Text
Article Information
| Title | Unitary representations of Poincaré
group ${\mathrm{P}(1,n)}$ in ${\mathrm{SO}(1,n)}$-basis |
| Source | Methods Funct. Anal. Topology, Vol. 27 (2021), no. 3, 258-276 |
| DOI | 10.31392/MFAT-npu26_3.2021.06 |
| MathSciNet |
MR4344365 |
| Milestones | Received 17/10/2020; Revised 05/11/2020 |
| Copyright | The Author(s) 2021 (CC BY-SA) |
Authors Information
Olha Ostrovska
National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Kyiv, Ukraine
Ivan I. Yuryk
National University of Food Technologies, Kyiv, Ukraine
Citation Example
Olha Ostrovska and Ivan I. Yuryk, Unitary representations of Poincaré
group ${\mathrm{P}(1,n)}$ in ${\mathrm{SO}(1,n)}$-basis, Methods Funct. Anal. Topology 27
(2021), no. 3, 258-276.
BibTex
@article {MFAT1632,
AUTHOR = {Olha Ostrovska and Ivan I. Yuryk},
TITLE = {Unitary representations of Poincaré
group ${\mathrm{P}(1,n)}$ in ${\mathrm{SO}(1,n)}$-basis},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {27},
YEAR = {2021},
NUMBER = {3},
PAGES = {258-276},
ISSN = {1029-3531},
MRNUMBER = {MR4344365},
DOI = {10.31392/MFAT-npu26_3.2021.06},
URL = {http://mfat.imath.kiev.ua/article/?id=1632},
}
