Open Access

Unitary representations of Poincaré group ${\mathrm{P}(1,n)}$ in ${\mathrm{SO}(1,n)}$-basis


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

TitleUnitary representations of Poincaré group ${\mathrm{P}(1,n)}$ in ${\mathrm{SO}(1,n)}$-basis
SourceMethods Funct. Anal. Topology, Vol. 27 (2021), no. 3, 258-276
MilestonesReceived 17/10/2020; Revised 05/11/2020
CopyrightThe 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

Google Scholar Metrics

Citing articles in Google Scholar
Similar articles in Google Scholar

Export article

Save to Mendeley

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.


@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},
       DOI = {10.31392/MFAT-npu26_3.2021.06},
       URL = {},


Coming Soon.

All Issues