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SIGMA 3 (2007), 117, 28 pages arXiv:0712.1107
https://doi.org/10.3842/SIGMA.2007.117
Contribution to the Proceedings of the Seventh International Conference Symmetry in Nonlinear Mathematical Physics
Self-Localized Quasi-Particle Excitation in Quantum Electrodynamics and Its Physical Interpretation
Ilya D. Feranchuk and Sergey I. Feranchuk
Department of Physics, Belarusian University, 4 Nezavisimosti Ave., 220030, Minsk, Belarus
Received October 21, 2007, in final form November 29, 2007; Published online December 07, 2007
Abstract
The self-localized quasi-particle excitation of the
electron-positron field (EPF) is found for the first time in
the framework of a standard form of the quantum electrodynamics.
This state is interpreted as the ''physical'' electron (positron)
and it allows one to solve the following problems: i) to express
the ''primary'' charge e0 and the mass m0 of the ''bare''
electron in terms of the observed values of e and m of the
''physical'' electron without any infinite parameters and by
essentially nonperturbative way; ii) to consider μ-meson as
another self-localized EPF state and to estimate the ratio
mμ/m; iii) to prove that the self-localized state is
Lorentz-invariant and its energy spectrum corresponds to the
relativistic free particle with the observed mass m; iv) to
show that the expansion in a power of the observed charge e <<
1 corresponds to the strong coupling expansion in a power of the
''primary'' charge e-10 ~ e when the interaction between
the ``physical'' electron and the transverse electromagnetic
field is considered by means of the perturbation theory and all
terms of this series are free from the ultraviolet divergence.
Key words:
renormalization; Dirac electron-positron vacuum; nonperturbative theory.
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References
- Weinberg S., Unified theories of elementary particle interactions, Scientific American 231 (1974), 50-58.
- Akhiezer A.I., Beresteckii V.B., Quantum
electrodynamics, Nauka, Moscow, 1969.
Bogoliubov N.N., Shirkov D.V., Introduction to the theory of
quantum fields, Nauka, Moscow, 1973.
- Scharf G., Finite quantum electrodynamics:
the causal approach, John Wiley and Sons, Inc., USA, 2001.
Scharf G., Quantum gauge theories: a true ghost
story, Springer Verlag, Berlin - Heidelberg - New York, 1995.
- Dirac P.A.M., The principles of quantum mechanics,
The Clarendon Press, Oxford, 1958.
- Feynman R.P., Nobel lecture, Science
153 (1966), 699-711.
- Lifshitz E.M., Pitaevskii L.P., Relativistic
quantum theory. Part II, Nauka, Moscow, 1971.
- Janke W., Pelster A., Schmidt H.-J., Bachmann M. (Editors), Fluctuating paths and fields,
Proceedings dedicated to Hagen Kleinert, World Scientific,
Singapore, 2001.
- Dirac P.A.M., An extensible model of the electron, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 268 (1962), 57-67.
- Klevansky S.P., The Nambu-Jona-Lasinio model of quantum chromodynamics,
Rev. Modern Phys. 64 (1992), 649-671.
Gusynin V.P., Miransky V.A., Shovkovy I.A., Large N dynamics in QED in a magnetic field, Phys. Rev. D 67 (2003), 107703, 4 pages, hep-ph/0304059.
- Hong D.K., Rajeev S.G., Towards a bosonization of quantum electrodynamics,
Phys. Rev. Lett. 21 (1990), 2475-2479.
- Miransky V.A., Dynamics of spontaneous chiral symmetry breaking and continuous
limit in quantum electrodynamics, Nuovo Cimento A 90
(1985), 149-160.
- Alexandrou C., Rosenfelder R., Schreiber A.W., Nonperturbative mass renormalization
in quenched QED from the worldline variational approach,
Phys. Rev. D 62 (2000), 085009, 10 pages.
- Pekar S.I., Autolocalization of the electron in the dielectric inertially polarized media, J. Exp. Theor. Phys. 16 (1946), 335-340.
- Bogoliubov N.N., About one new form of the adiabatic perturbation theory in the problem
of interaction between particle and quantum field, Uspekhi Mat. Nauk 2 (1950), 3-24.
Tyablikov S.V., Adiabatic form of the perturbation theory in the
problem of interaction between paricle and quantum field,
J. Exp. Theor. Phys. 21 (1951), 377-388.
- Dodd R.K., Eilbeck J.C., Gibbon J.D., Moris H.C.,
Solitons and nonlinear wave equations, Academic Press, London,
1984.
- Fröhlich H., Electrons in lattice fields, Adv. Phys.
3 (1954), 325-361.
- Heitler W., The quantum theory of radiation,
The Clarendon Press, Oxford, 1954.
- Landau L.D., Lifshitz E.M., Quantum mechanics, Nauka, Moscow, 1963.
- Gross E.P., Strong coupling polaron theory and translational invariance, Ann. Physics,
99 (1976), 1-29.
- Bagan E., Lavelle M., McMullan D., Charges from dressed matter:
physics and renormalization, Ann. Physics, 282
(2000), 503-540,
hep-ph/9909262.
- Yukalov V.I., Nonperturbative theory for anharmonic oscillator, Theoret. and Math. Phys.
28 (1976), 652-660.
Caswell W.E., Accurate energy levels for the anharmonic oscillator and series for the double-well potential in perturbation theory, Ann. Physics 123 (1979), 153-182.
- Feranchuk I.D., Komarov L.I., The operator method of the approximate solution of the
Schrödinger equation, Phys. Lett. A 88 (1982),
211-214.
- Feranchuk I.D., Komarov L.I., Nichipor I.V.,
Ulyanenkov A.P., Operator method in the problem of quantum anharmonic oscillator,
Ann. Physics 238 (1995), 370-440.
- Feranchuk I.D., Komarov L.I.,
Ulyanenkov A.P., Two-level system in a one-mode quantum field: numerical solution on the basis
of the operator method, J. Phys. A: Math. Gen. 29 (1996), 4035-4047.
- Feranchuk I.D., Komarov L.I.,
Ulyanenkov A.P., A new method for calculation of crystal susceptibilities for x-ray diffraction
at arbitrary wavelength, Acta Crystallogr. Sect. A 58 (2002), 370-384.
- Fradkin E.S., Renormalization in quantum electrodynamics with self-consistent field,
Proc. Fiz. Inst.
of Soviet Academy of Science 29 (1965), 1-154.
Fradkin E.S., Application of functional methods in quantum field theory and quantum statistics, Nuclear Phys. 76 (1966), 588-612.
- Bogoliubov N.N., Quasi-mean values in the problems
of statistical mechanics. Selected Works, Vol. 3, Naukova Dumka,
Kiev, 1971.
- Komarov L.I., Krylov E.V., Feranchuk I.D., Numerical solution of the nonlinear eigenvalue
problem, Zh. Vychisl. Mat. Mat. Fiz. 18 (1978),
681-691.
- Feranchuk I.D., Feranchuk S.I., Self-consistent state in the strong-coupling QED,
hep-th/0309072.
- Bawin M., Lavine J.D., On the existence of a critical charge for superheavy nucleus,
Nuovo Cimento 15 (1973), 38-44.
- Feranchuk I.D., Finite electron charge and mass renormalization in quantum electrodynamics,
math-ph/0605028.
- Shnir Ya.M., Monopol,
Springer, Berlin, 2005.
- Brodsky S.J., Drell S.D., Anomalous magnetic moment and limits on fermion substructure,
Phys. Rev. D 22 (1980), 2236-2242.
- Feynman R.P., Slow electrons in a polar crystal, Phys. Rev.
97 (1955), 660-665.
- Landau L.D., Pekar S.I., Effective mass of the polaron, J. Exp. Theor. Phys.
18 (1948), 419-423.
- Eides M.I., Grotch H., Shelyuto V.A., Theory of light hydrogenlike atoms,
Phys. Rep. 342 (2001), 63-261,
hep-ph/0002158.
- Bjorken J.D., Drell S.D., Relativistic quantum mechanics, McGraw-Hill Book Company, London, 1976.
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