RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 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

 TMF, 2004, Volume 141, Number 3, Pages 424–454 (Mi tmf131)

Algebra with Quadratic Commutation Relations for an Axially Perturbed Coulomb–Dirac Field

M. V. Karasev, E. M. Novikova

Moscow State Institute of Electronics and Mathematics

Abstract: The motion of a particle in the field of an electromagnetic monopole (in the Coulomb–Dirac field) perturbed by an axially symmetric potential after quantum averaging is described by an integrable system. Its Hamiltonian can be written in terms of the generators of an algebra with quadratic commutation relations. We construct the irreducible representations of this algebra in terms of second-order differential operators; we also construct its hypergeometric coherent states. We use these states in the first-order approximation with respect to the perturbing field to obtain the integral representation of the eigenfunctions of the original problem in terms of solutions of the model Heun-type second-order ordinary differential equation and present the asymptotic approximation of the corresponding eigenvalues.

Keywords: integrable systems, Dirac monopole, nonlinear commutation relations, coherent states, asymptotic spectrum behavior

DOI: https://doi.org/10.4213/tmf131

Full text: PDF file (413 kB)
References: PDF file   HTML file

English version:
Theoretical and Mathematical Physics, 2004, 141:3, 1698–1724

Bibliographic databases:

Citation: M. V. Karasev, E. M. Novikova, “Algebra with Quadratic Commutation Relations for an Axially Perturbed Coulomb–Dirac Field”, TMF, 141:3 (2004), 424–454; Theoret. and Math. Phys., 141:3 (2004), 1698–1724

Citation in format AMSBIB
\Bibitem{KarNov04} \by M.~V.~Karasev, E.~M.~Novikova \paper Algebra with Quadratic Commutation Relations for an Axially Perturbed Coulomb--Dirac Field \jour TMF \yr 2004 \vol 141 \issue 3 \pages 424--454 \mathnet{http://mi.mathnet.ru/tmf131} \crossref{https://doi.org/10.4213/tmf131} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2141137} \zmath{https://zbmath.org/?q=an:1178.81133} \adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2004TMP...141.1698K} \elib{https://elibrary.ru/item.asp?id=13445814} \transl \jour Theoret. and Math. Phys. \yr 2004 \vol 141 \issue 3 \pages 1698--1724 \crossref{https://doi.org/10.1023/B:TAMP.0000049763.86662.16} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000226332800007} 

• http://mi.mathnet.ru/eng/tmf131
• https://doi.org/10.4213/tmf131
• http://mi.mathnet.ru/eng/tmf/v141/i3/p424

 SHARE:

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. Karasev M., “Birkhoff resonances and quantum ray method”, Days on Diffraction 2004, Proceedings, 2004, 114–126
2. M. V. Karasev, E. M. Novikova, “Algebra with polynomial commutation relations for the Zeeman effect in the Coulomb–Dirac field”, Theoret. and Math. Phys., 142:1 (2005), 109–127
3. M. V. Karasev, E. M. Novikova, “Algebra with polynomial commutation relations for the Zeeman–Stark effect in the hydrogen atom”, Theoret. and Math. Phys., 142:3 (2005), 447–469
4. A. V. Pereskokov, “Asymptotics of the Spectrum and Quantum Averages near the Boundaries of Spectral Clusters for Perturbed Two-Dimensional Oscillators”, Math. Notes, 92:4 (2012), 532–543
5. A. V. Pereskokov, “Asymptotics of the spectrum of the hydrogen atom in a magnetic field near the lower boundaries of spectral clusters”, Trans. Moscow Math. Soc., 73 (2012), 221–262
6. A. V. Pereskokov, “Asymptotics of the spectrum and quantum averages of a perturbed resonant oscillator near the boundaries of spectral clusters”, Izv. Math., 77:1 (2013), 163–210
•  Number of views: This page: 361 Full text: 170 References: 51 First page: 1