On the Perturbation Theory in Quantum Electrodynamics Using the Wave Functions of the Dressed States

Yuriy N. Zayko

doi:doi:10.11648/j.ijamtp.20160204.11

| Peer-Reviewed

On the Perturbation Theory in Quantum Electrodynamics Using the Wave Functions of the Dressed States

Yuriy N. Zayko

Published in International Journal of Applied Mathematics and Theoretical Physics (Volume 2, Issue 4)

Received: 4 August 2016 Accepted: 15 August 2016 Published: 6 September 2016

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

Abstract

The paper considers the possibility of constructing a perturbation theory for problems of quantum electrodynamics, which is based on the wave functions of so-called "dressed" electron, unlike traditional perturbation theory, which uses the wave functions of the "bare" electrons. To investigate the wave functions of the "dressed" electron a numerical investigation of associated Dirac-Maxwell equations was performed in the approximation of small electron pulses. An expression for the energy eigenvalues of the considered self-consistent problem was found in a quasi-classical approximation as well as an estimation of the lifetime of the "dressed" electron and the effective value of the electron charge.

Published in	International Journal of Applied Mathematics and Theoretical Physics (Volume 2, Issue 4)
DOI	10.11648/j.ijamtp.20160204.11
Page(s)	28-30
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Photon, Electron, Quantum Electrodynamics, Perturbation Theory, Divergence, Renormalization

References

[1]	Rajaraman R. An Introduction to Solitons and Instantons in Quantum Field Theory. North-Holland Publishing Company, Amsterdam-NY-Oxford (1982).
[2]	Zee A., Quantum Field Theory in a Nutshell. 2nd ed. Princeton University Press, 2007.
[3]	Feinberg E. L. Uspekhi Fizicheskih Nauk, V. 132, № 2, pp. 255-291, 1980 (Russian).
[4]	Berestetskii V. B., Lifshitz E. M., Pitaevskii L. P., (1971). Relativistic Quantum Theory. Vol. 4 (1st ed.). Pergamon Press.
[5]	Bohm D., Quantum Theory. New York: Prentice Hall; 1989
[6]	Harrison R, Moroz I. and Tod K. P.. A numerical study of the Schrȍdinger–Newton equations, Nonlinearity V. 16, p.101–122, 2003.
[7]	Moroz M., Penrose R. and Tod P. Spherically-symmetric solutions of the Schrȍdinger–Newton equations, Class. Quantum Grav. V. 15 2733–2742, 1998.
[8]	Landau L. D., Pomeranchuk I. Ya. On the point-like interaction in quantum electrodynamics. Doklady Akademii Nauk USSR, (1955), V. 102, p. 489.(Russian).
[9]	Hu H. and Yuan J. Non-perturbative QED Model with Dressed States to Tackle HHG in Ultrashort Intense Laser Pulses.- Phys. Rev. A 78, 063826, 2008.
[10]	Lindgren I., Salomonson S. and Holmberg J. Energy-dependent perturbation theory: Possibility for improved tests of quantum-electrodynamics.- arXiv:1212.6482, (28.12.2012)
[11]	Neznamov V. P. Anomalous magnetic moment and Lamb shift in the second order of the perturbation theory with finite electron mass renormalization in QED. arXiv: hep-th/0403125v2, (20.04.2004).
[12]	Jentschura U. D. Quantum Electrodynamic Bound-State Calculations and Large-Order Perturbation Theory. arXiv: hep-ph/0306153, (27.04.2004).

Cite This Article

Plain Text BibTeX RIS

APA Style

Yuriy N. Zayko. (2016). On the Perturbation Theory in Quantum Electrodynamics Using the Wave Functions of the Dressed States. International Journal of Applied Mathematics and Theoretical Physics, 2(4), 28-30. https://doi.org/10.11648/j.ijamtp.20160204.11

Copy | Download

ACS Style

Yuriy N. Zayko. On the Perturbation Theory in Quantum Electrodynamics Using the Wave Functions of the Dressed States. Int. J. Appl. Math. Theor. Phys. 2016, 2(4), 28-30. doi: 10.11648/j.ijamtp.20160204.11

Copy | Download

AMA Style

Yuriy N. Zayko. On the Perturbation Theory in Quantum Electrodynamics Using the Wave Functions of the Dressed States. Int J Appl Math Theor Phys. 2016;2(4):28-30. doi: 10.11648/j.ijamtp.20160204.11

Copy | Download

@article{10.11648/j.ijamtp.20160204.11,
  author = {Yuriy N. Zayko},
  title = {On the Perturbation Theory in Quantum Electrodynamics Using the Wave Functions of the Dressed States},
  journal = {International Journal of Applied Mathematics and Theoretical Physics},
  volume = {2},
  number = {4},
  pages = {28-30},
  doi = {10.11648/j.ijamtp.20160204.11},
  url = {https://doi.org/10.11648/j.ijamtp.20160204.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijamtp.20160204.11},
  abstract = {The paper considers the possibility of constructing a perturbation theory for problems of quantum electrodynamics, which is based on the wave functions of so-called "dressed" electron, unlike traditional perturbation theory, which uses the wave functions of the "bare" electrons. To investigate the wave functions of the "dressed" electron a numerical investigation of associated Dirac-Maxwell equations was performed in the approximation of small electron pulses. An expression for the energy eigenvalues of the considered self-consistent problem was found in a quasi-classical approximation as well as an estimation of the lifetime of the "dressed" electron and the effective value of the electron charge.},
 year = {2016}
}

Copy | Download

TY  - JOUR
T1  - On the Perturbation Theory in Quantum Electrodynamics Using the Wave Functions of the Dressed States
AU  - Yuriy N. Zayko
Y1  - 2016/09/06
PY  - 2016
N1  - https://doi.org/10.11648/j.ijamtp.20160204.11
DO  - 10.11648/j.ijamtp.20160204.11
T2  - International Journal of Applied Mathematics and Theoretical Physics
JF  - International Journal of Applied Mathematics and Theoretical Physics
JO  - International Journal of Applied Mathematics and Theoretical Physics
SP  - 28
EP  - 30
PB  - Science Publishing Group
SN  - 2575-5927
UR  - https://doi.org/10.11648/j.ijamtp.20160204.11
AB  - The paper considers the possibility of constructing a perturbation theory for problems of quantum electrodynamics, which is based on the wave functions of so-called "dressed" electron, unlike traditional perturbation theory, which uses the wave functions of the "bare" electrons. To investigate the wave functions of the "dressed" electron a numerical investigation of associated Dirac-Maxwell equations was performed in the approximation of small electron pulses. An expression for the energy eigenvalues of the considered self-consistent problem was found in a quasi-classical approximation as well as an estimation of the lifetime of the "dressed" electron and the effective value of the electron charge.
VL  - 2
IS  - 4
ER  -

Copy | Download

Author Information

Yuriy N. Zayko

Department of Applied Informatics, Faculty of Public Administration, Russian Presidential Academy of National Economy and Public Administration, Stolypin Volga Region Institute, Saratov, Russia

Download PDF

Sections

Plain Text BibTeX RIS

APA Style

Yuriy N. Zayko. (2016). On the Perturbation Theory in Quantum Electrodynamics Using the Wave Functions of the Dressed States. International Journal of Applied Mathematics and Theoretical Physics, 2(4), 28-30. https://doi.org/10.11648/j.ijamtp.20160204.11

Copy | Download

ACS Style

Yuriy N. Zayko. On the Perturbation Theory in Quantum Electrodynamics Using the Wave Functions of the Dressed States. Int. J. Appl. Math. Theor. Phys. 2016, 2(4), 28-30. doi: 10.11648/j.ijamtp.20160204.11

Copy | Download

AMA Style

Yuriy N. Zayko. On the Perturbation Theory in Quantum Electrodynamics Using the Wave Functions of the Dressed States. Int J Appl Math Theor Phys. 2016;2(4):28-30. doi: 10.11648/j.ijamtp.20160204.11

Copy | Download

@article{10.11648/j.ijamtp.20160204.11,
  author = {Yuriy N. Zayko},
  title = {On the Perturbation Theory in Quantum Electrodynamics Using the Wave Functions of the Dressed States},
  journal = {International Journal of Applied Mathematics and Theoretical Physics},
  volume = {2},
  number = {4},
  pages = {28-30},
  doi = {10.11648/j.ijamtp.20160204.11},
  url = {https://doi.org/10.11648/j.ijamtp.20160204.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijamtp.20160204.11},
  abstract = {The paper considers the possibility of constructing a perturbation theory for problems of quantum electrodynamics, which is based on the wave functions of so-called "dressed" electron, unlike traditional perturbation theory, which uses the wave functions of the "bare" electrons. To investigate the wave functions of the "dressed" electron a numerical investigation of associated Dirac-Maxwell equations was performed in the approximation of small electron pulses. An expression for the energy eigenvalues of the considered self-consistent problem was found in a quasi-classical approximation as well as an estimation of the lifetime of the "dressed" electron and the effective value of the electron charge.},
 year = {2016}
}

Copy | Download

TY  - JOUR
T1  - On the Perturbation Theory in Quantum Electrodynamics Using the Wave Functions of the Dressed States
AU  - Yuriy N. Zayko
Y1  - 2016/09/06
PY  - 2016
N1  - https://doi.org/10.11648/j.ijamtp.20160204.11
DO  - 10.11648/j.ijamtp.20160204.11
T2  - International Journal of Applied Mathematics and Theoretical Physics
JF  - International Journal of Applied Mathematics and Theoretical Physics
JO  - International Journal of Applied Mathematics and Theoretical Physics
SP  - 28
EP  - 30
PB  - Science Publishing Group
SN  - 2575-5927
UR  - https://doi.org/10.11648/j.ijamtp.20160204.11
AB  - The paper considers the possibility of constructing a perturbation theory for problems of quantum electrodynamics, which is based on the wave functions of so-called "dressed" electron, unlike traditional perturbation theory, which uses the wave functions of the "bare" electrons. To investigate the wave functions of the "dressed" electron a numerical investigation of associated Dirac-Maxwell equations was performed in the approximation of small electron pulses. An expression for the energy eigenvalues of the considered self-consistent problem was found in a quasi-classical approximation as well as an estimation of the lifetime of the "dressed" electron and the effective value of the electron charge.
VL  - 2
IS  - 4
ER  -

Copy | Download