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TMF, 2009, Volume 158, Number 2, Pages 250–262 (Mi tmf6312)  

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

Spontaneous fermion creation in the Coulomb field and Aharonov–Bohm potential in $2+1$ dimensions

V. R. Khalilov

M. V. Lomonosov Moscow State University

Abstract: We find exact solutions of the Dirac equation and the fermion energy spectrum in the Coulomb (vector and scalar) potential and Aharonov–Bohm potential in $2+1$ dimensions taking the particle spin into account. We describe the fermion spin using the two-component Dirac equation with the additional (spin) parameter introduced by Hagen. We consider the effect of creation of fermion pairs from the vacuum by a strong Coulomb field in the Aharonov–Bohm potential in $2+1$ dimensions. We obtain transcendental equations implicitly determining the electron energy spectrum near the boundary of the lower energy continuum and the critical charge. We numerically solve the equation for the critical charge. We show that for relatively weak magnetic flows, the critical charge decreases (compared with the case with no magnetic field) if the energy of interaction of the electron spin magnetic moment with the magnetic field is negative and increases if this energy is positive.

Keywords: spin, Coulomb field, Aharonov–Bohm potential, bound state, energy spectrum, lower continuum, critical charge, pair creation

DOI: https://doi.org/10.4213/tmf6312

Full text: PDF file (423 kB)
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English version:
Theoretical and Mathematical Physics, 2009, 158:2, 210–220

Bibliographic databases:

Received: 23.04.2008

Citation: V. R. Khalilov, “Spontaneous fermion creation in the Coulomb field and Aharonov–Bohm potential in $2+1$ dimensions”, TMF, 158:2 (2009), 250–262; Theoret. and Math. Phys., 158:2 (2009), 210–220

Citation in format AMSBIB
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  • http://mi.mathnet.ru/eng/tmf/v158/i2/p250

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    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. Khalilov V.R., Lee K.E., “Bound Fermion States in a Vector 1/R and Aharonov-Bohm Potential in (2+1) Dimensions”, Modern Phys Lett A, 26:12 (2011), 865–883  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    2. V. R. Khalilov, K. E. Lee, “Discrete spectra of the Dirac Hamiltonian in Coulomb and Aharonov–Bohm potentials in $2+1$ dimensions”, Theoret. and Math. Phys., 169:3 (2011), 1683–1703  mathnet  crossref  crossref  isi
    3. V. R. Khalilov, “Zero-mass fermions in Coulomb and Aharonov–Bohm potentials in 2+1 dimensions”, Theoret. and Math. Phys., 175:2 (2013), 637–654  mathnet  crossref  crossref  zmath  adsnasa  isi  elib  elib
    4. Khalilov V.R., “Creation of Planar Charged Fermions in Coulomb and Aharonov-Bohm Potentials”, Eur. Phys. J. C, 73:8 (2013), 2548  crossref  adsnasa  isi  scopus  scopus
    5. I. V. Mamsurov, V. R. Khalilov, “Induced vacuum charge of massless fermions in Coulomb and Aharonov–Bohm potentials in $2+1$ dimensions”, Theoret. and Math. Phys., 188:2 (2016), 1181–1196  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    6. Oliveira R.R.S., Maluf R.V., Almeida C.A.S., “Bound-State Solutions of the Dirac Oscillator in An Aharonov-Bohm-Coulomb System”, Ann. Phys., 400 (2019), 1–8  crossref  mathscinet  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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