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, 2011, Volume 167, Number 2, Pages 171–192 (Mi tmf6632)  

This article is cited in 6 scientific papers (total in 6 papers)

Generalized Foldy–Wouthuysen transformation and pseudodifferential operators

J. Brüninga, V. V. Grushinbc, S. Yu. Dobrokhotovbd, T. Ya. Tudorovskiie

a Humboldt University, Berlin, Germany
b Moscow Institute for Physics and Technology, Moscow, Russia
c Moscow State Institute for Electronics and Mathematics, Moscow, Russia
d Ishlinskii Institute for Problems in Mechanics, RAS, Moscow, Russia
e Institute for Molecules and Materials Radboud, University of Nijmegen, Nijmegen, The~Netherlands

Abstract: We show that the Foldy–Wouthuysen transformation and its generalizations are simplified if the methods of pseudodifferential operators are used, which also allow estimating the exactness of the transition from the Dirac equation to the reduced equations for electrons and positrons. The methods and techniques used can be useful not only in studying asymptotic solutions of the Dirac equation but also in other problems.

Keywords: Dirac equation, Foldy–Wouthuysen transformation, adiabatic approximation, pseudodifferential operator

DOI: https://doi.org/10.4213/tmf6632

Full text: PDF file (557 kB)
References: PDF file   HTML file

English version:
Theoretical and Mathematical Physics, 2011, 167:2, 547–566

Bibliographic databases:

Document Type: Article
Received: 16.11.2010

Citation: J. Brüning, V. V. Grushin, S. Yu. Dobrokhotov, T. Ya. Tudorovskii, “Generalized Foldy–Wouthuysen transformation and pseudodifferential operators”, TMF, 167:2 (2011), 171–192; Theoret. and Math. Phys., 167:2 (2011), 547–566

Citation in format AMSBIB
\Bibitem{BruGruDob11}
\by J.~Br\"uning, V.~V.~Grushin, S.~Yu.~Dobrokhotov, T.~Ya.~Tudorovskii
\paper Generalized Foldy--Wouthuysen transformation and pseudodifferential operators
\jour TMF
\yr 2011
\vol 167
\issue 2
\pages 171--192
\mathnet{http://mi.mathnet.ru/tmf6632}
\crossref{https://doi.org/10.4213/tmf6632}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3166363}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2011TMP...167..547B}
\transl
\jour Theoret. and Math. Phys.
\yr 2011
\vol 167
\issue 2
\pages 547--566
\crossref{https://doi.org/10.1007/s11232-011-0041-y}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000291480900002}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-79958228250}


Linking options:
  • http://mi.mathnet.ru/eng/tmf6632
  • https://doi.org/10.4213/tmf6632
  • http://mi.mathnet.ru/eng/tmf/v167/i2/p171

    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

    This publication is cited in the following articles:
    1. J. Brüning, V. V. Grushin, S. Yu. Dobrokhotov, “Averaging of Linear Operators, Adiabatic Approximation, and Pseudodifferential Operators”, Math. Notes, 92:2 (2012), 151–165  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    2. V. V. Grushin, S. Yu. Dobrokhotov, S. A. Sergeev, “Homogenization and dispersion effects in the problem of propagation of waves generated by a localized source”, Proc. Steklov Inst. Math., 281 (2013), 161–178  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    3. V. V. Grushin, S. Yu. Dobrokhotov, “Homogenization in the Problem of Long Water Waves over a Bottom Site with Fast Oscillations”, Math. Notes, 95:3 (2014), 324–337  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    4. Ampilogov D., Leble S., “Directed electromagnetic wave propagation in 1D metamaterial: Projecting operators method”, Phys. Lett. A, 380:29-30 (2016), 2271–2278  crossref  mathscinet  isi  elib  scopus
    5. Dobrokhotov S.Yu., Grushin V.V., Sergeev S.A., Tirozzi B., “Asymptotic theory of linear water waves in a domain with nonuniform bottom with rapidly oscillating sections”, Russ. J. Math. Phys., 23:4 (2016), 455–474  crossref  mathscinet  zmath  isi  elib  scopus
    6. Reijnders K.J.A., Minenkov D.S., Katsnelson I M., Dobrokhotov S.Yu., “Electronic Optics in Graphene in the Semiclassical Approximation”, Ann. Phys., 397 (2018), 65–135  crossref  mathscinet  zmath  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
    Number of views:
    This page:359
    Full text:79
    References:37
    First page:24

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