A New Family of Interactions between Clothed Particles in QED
DOI:
https://doi.org/10.15407/ujpe66.10.833Keywords:
unitary clothing transformations, quantum electrodynamics, clothed particles, off-energy-shell effectsAbstract
The method of unitary clothing transformations (UCTs) has been applied to the quantum electrodynamics (QED) by using the clothed particle representation (CPR). Within CPR, the Hamiltonian for interacting electromagnetic and electron-positron fields takes the form in which the interaction operators responsible for such two-particle processes as e−e− → e−e−, e+e+ → e+e+, e−e+ → e−e+, e−e+ → yy, yy → e−e+, ye− → ye−, and ye+ → ye+ are obtained on the same physical footing. These novel interactions include the off-energy-shell and recoil effects (the latter without any expansion in (v/c)2-series) and their on-energy shell matrix elements reproduce the well-known results derived within the perturbation theory based on the Dyson expansion for the S-matrix (in particular, the Møller formula for the e−e−-scattering, the Bhabha formula for e−e+-scattering, and the Klein–Nishina one for the Compton scattering).
References
O. Greenberg, S. Schweber. Clothed particle operators in simple models of quantum field theory. Nuovo Cim. 8, 378 (1958).
https://doi.org/10.1007/BF02828746
A. Shebeko, M. Shirokov. Clothing procedure in relativistic quantum field theory and its applications to description of electromagnetic interactions with nuclei (bound systems). Progr. Part. Nucl. Phys. 44, 75 (2000).
https://doi.org/10.1016/S0146-6410(00)00060-0
A. Shebeko, M. Shirokov. Unitary transformations in quantum field theory and bound states. Phys. Part. Nucl. 32, 15 (2001) [arXiv: nucl-th/0102037].
V. Korda, A. Shebeko. Clothed particles representation in quantum field theory: mass renormalization. Phys. Rev. D 70, 085011 (2004).
https://doi.org/10.1103/PhysRevD.70.085011
V. Korda, L. Canton, A. Shebeko. Relativistic interactions for the meson-two-nucleon system in the clothed-particle unitary representation. Ann. Phys. 322, 736 (2007).
https://doi.org/10.1016/j.aop.2006.07.010
I. Dubovyk, A. Shebeko. The method of unitary clothing transformations in the theory of nucleon-nucleon scattering. Few-Body Syst. 48, 109 (2010).
https://doi.org/10.1007/s00601-010-0097-5
E. Dubovyk, A. Shebeko. Low-energy parameters of the nucleon-nucleon scattering and deuteron properties, electromagnetic interactions with bound systems. Few-Body Syst. 54, 1513 (2013).
https://doi.org/10.1007/s00601-012-0559-z
A. Shebeko. The method of unitary clothing transformations in relativistic quantum field theory: Recent applications for the description of nucleon-nucleon scattering and deuteron properties. Few-Body Syst. 54, 2271 (2013).
https://doi.org/10.1007/s00601-012-0482-3
H. Kamada, A. Shebeko, A. Arslanaliev. Triton binding energy of Kharkov potential. Few-Body Syst. 58, 70 (2017).
https://doi.org/10.1007/s00601-017-1241-2
A. Shebeko. Clothed particles in mesodynamics, quantum electrodynamics and other field models. PoS Baldin ISHEPP XXII 225, 027 (2015).
https://doi.org/10.22323/1.225.0027
A. Shebeko. Clothed particles in quantum electrodynamics and quantum chromodynamics. EPJ Web Conf. 113, 03014 (2016).
https://doi.org/10.1051/epjconf/201611303014
A. Arslanaliev, Y. Kostylenko, A. Shebeko. QED in the clothed-particle representation. In: Recent Progress in Few-Body Physics. Edited by N. Orr et al. (Springer, 2020), p. 41.
https://doi.org/10.1007/978-3-030-32357-8_8
Y. Kostylenko, A. Arslanaliev, A. Shebeko. QED in the clothed-particle representation: A fresh look at positronium properties treatment. SciPost Phys. Proc. 3, 45 (2020).
https://doi.org/10.21468/SciPostPhysProc.3.045
S. Weinberg. The Quantum Theory of Fields (Cambridge University Press, 1995), Vol.1.
https://doi.org/10.1017/CBO9781139644167
A. Shebeko, P. Frolov. A possible way for constructing generators of the Poincar'e group in quantum field theory. FewBody Syst. 52, 125 (2012).
https://doi.org/10.1007/s00601-011-0262-5
E. Stefanovich. Relativistic quantum dynamics: A nontraditional perspective on space, time, particles, fields, and action-at-a-distance. Ann. Phys. 322 (2007) [arXiv: physics/0504062].
S. Schweber. An Introduction to Relativistic Quantum Field Theory (Row, Peterson & Co., 1961) [ISBN: 978-0486442280].
A. Arslanaliev. MSc thesis. The Method of Unitary Clothing Transformations: Application in Quantum Electrodynamics (V.N. Karazin National University, 2017).
Y. Kostylenko. MSc thesis. The Application of the Method of Unitary Clothing Transformations in the Description of Positronium Properties (V.N. Karazin National University, 2019).
H. Kleinert. Particles and Quantum Fields (Freie Universit¨at, 2016).
M. Goldberger, K. Watson. Collision Theory (Wiley, 1967).
A. Shebeko. The S-matrix in the method of unitary clothing transformations. Nucl. Phys. A 737, 252 (2004).
Downloads
Published
How to Cite
Issue
Section
License
Copyright Agreement
License to Publish the Paper
Kyiv, Ukraine
The corresponding author and the co-authors (hereon referred to as the Author(s)) of the paper being submitted to the Ukrainian Journal of Physics (hereon referred to as the Paper) from one side and the Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, represented by its Director (hereon referred to as the Publisher) from the other side have come to the following Agreement:
1. Subject of the Agreement.
The Author(s) grant(s) the Publisher the free non-exclusive right to use the Paper (of scientific, technical, or any other content) according to the terms and conditions defined by this Agreement.
2. The ways of using the Paper.
2.1. The Author(s) grant(s) the Publisher the right to use the Paper as follows.
2.1.1. To publish the Paper in the Ukrainian Journal of Physics (hereon referred to as the Journal) in original language and translated into English (the copy of the Paper approved by the Author(s) and the Publisher and accepted for publication is a constitutive part of this License Agreement).
2.1.2. To edit, adapt, and correct the Paper by approval of the Author(s).
2.1.3. To translate the Paper in the case when the Paper is written in a language different from that adopted in the Journal.
2.2. If the Author(s) has(ve) an intent to use the Paper in any other way, e.g., to publish the translated version of the Paper (except for the case defined by Section 2.1.3 of this Agreement), to post the full Paper or any its part on the web, to publish the Paper in any other editions, to include the Paper or any its part in other collections, anthologies, encyclopaedias, etc., the Author(s) should get a written permission from the Publisher.
3. License territory.
The Author(s) grant(s) the Publisher the right to use the Paper as regulated by sections 2.1.1–2.1.3 of this Agreement on the territory of Ukraine and to distribute the Paper as indispensable part of the Journal on the territory of Ukraine and other countries by means of subscription, sales, and free transfer to a third party.
4. Duration.
4.1. This Agreement is valid starting from the date of signature and acts for the entire period of the existence of the Journal.
5. Loyalty.
5.1. The Author(s) warrant(s) the Publisher that:
– he/she is the true author (co-author) of the Paper;
– copyright on the Paper was not transferred to any other party;
– the Paper has never been published before and will not be published in any other media before it is published by the Publisher (see also section 2.2);
– the Author(s) do(es) not violate any intellectual property right of other parties. If the Paper includes some materials of other parties, except for citations whose length is regulated by the scientific, informational, or critical character of the Paper, the use of such materials is in compliance with the regulations of the international law and the law of Ukraine.
6. Requisites and signatures of the Parties.
Publisher: Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine.
Address: Ukraine, Kyiv, Metrolohichna Str. 14-b.
Author: Electronic signature on behalf and with endorsement of all co-authors.
.png){kind=small}
