RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



TMF:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


TMF, 2018, Volume 195, Number 3, Pages 331–361 (Mi tmf9503)  

Unitary representations of the Wigner group $ISL(2,\mathbb C)$ and a two-spinor description of massive particles with an arbitrary spin

A. P. Isaevab, M. A. Podoinicinab

a Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna, Moscow Oblast, Russia
b Dubna State University, Dubna, Moscow Oblast, Russia

Abstract: Based on Wigner unitary representations for the covering group $ISL(2,\mathbb C)$ of the Poincaré group, we obtain spin-tensor wave functions of free massive particles with an arbitrary spin that satisfy the Dirac–Pauli–Fierz equations. In the framework of a two-spinor formalism, we construct spin-polarization vectors and obtain conditions that fix the corresponding density matrices (the Berends–Fronsdal projection operators) determining the numerators in the propagators of the fields of such particles. Using these conditions, we find explicit expressions for the particle density matrices with integer (Berends–Fronsdal projection operators) and half-integer spin. We obtain a generalization of the Berens–Fronsdal projection operators to the case of an arbitrary number $D$ of space–time dimensions.

Keywords: Wigner unitary representation, Poincaré group, Berends–Fronsdal projection operator, Dirac–Pauli–Fierz equation.

Funding Agency Grant Number
Russian Science Foundation 14-11-00598
This research was supported by a grant from the Russian Science Foundation (Project No. 14-11-00598).


DOI: https://doi.org/10.4213/tmf9503

Full text: PDF file (646 kB)
First page: PDF file
References: PDF file   HTML file

English version:
Theoretical and Mathematical Physics, 2018, 195:3, 779–806

Bibliographic databases:

Document Type: Article
PACS: 10
MSC: 81Txx
Received: 28.10.2017

Citation: A. P. Isaev, M. A. Podoinicin, “Unitary representations of the Wigner group $ISL(2,\mathbb C)$ and a two-spinor description of massive particles with an arbitrary spin”, TMF, 195:3 (2018), 331–361; Theoret. and Math. Phys., 195:3 (2018), 779–806

Citation in format AMSBIB
\Bibitem{IsaPod18}
\by A.~P.~Isaev, M.~A.~Podoinicin
\paper Unitary representations of the~Wigner group $ISL(2,\mathbb C)$ and a~two-spinor description of~massive particles with an~arbitrary spin
\jour TMF
\yr 2018
\vol 195
\issue 3
\pages 331--361
\mathnet{http://mi.mathnet.ru/tmf9503}
\crossref{https://doi.org/10.4213/tmf9503}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2018TMP...195..779I}
\elib{http://elibrary.ru/item.asp?id=34940703}
\transl
\jour Theoret. and Math. Phys.
\yr 2018
\vol 195
\issue 3
\pages 779--806
\crossref{https://doi.org/10.1134/S0040577918060016}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000437754600001}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85049559023}


Linking options:
  • http://mi.mathnet.ru/eng/tmf9503
  • https://doi.org/10.4213/tmf9503
  • http://mi.mathnet.ru/eng/tmf/v195/i3/p331

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
    Number of views:
    This page:113
    References:7
    First page:8

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019