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


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.


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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
DOI10.31392/MFAT-npu26_3.2021.06
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


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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},
       DOI = {10.31392/MFAT-npu26_3.2021.06},
       URL = {http://mfat.imath.kiev.ua/article/?id=1632},
}


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