A New Family of Interactions between Clothed Particles in QED





unitary clothing transformations, quantum electrodynamics, clothed particles, off-energy-shell effects


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 ee → ee, e+e+ → e+e+, ee+ → ee+, ee+ → yy, yy → ee+, 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 ee-scattering, the Bhabha formula for ee+-scattering, and the Klein–Nishina one for the Compton scattering).


O. Greenberg, S. Schweber. Clothed particle operators in simple models of quantum field theory. Nuovo Cim. 8, 378 (1958).


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).


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).


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).


I. Dubovyk, A. Shebeko. The method of unitary clothing transformations in the theory of nucleon-nucleon scattering. Few-Body Syst. 48, 109 (2010).


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).


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).


H. Kamada, A. Shebeko, A. Arslanaliev. Triton binding energy of Kharkov potential. Few-Body Syst. 58, 70 (2017).


A. Shebeko. Clothed particles in mesodynamics, quantum electrodynamics and other field models. PoS Baldin ISHEPP XXII 225, 027 (2015).


A. Shebeko. Clothed particles in quantum electrodynamics and quantum chromodynamics. EPJ Web Conf. 113, 03014 (2016).


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.


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).


S. Weinberg. The Quantum Theory of Fields (Cambridge University Press, 1995), Vol.1.


A. Shebeko, P. Frolov. A possible way for constructing generators of the Poincar'e group in quantum field theory. FewBody Syst. 52, 125 (2012).


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).




How to Cite

Arslanaliev, A., Kostylenko, Y., & Shebeko, O. (2021). A New Family of Interactions between Clothed Particles in QED. Ukrainian Journal of Physics, 66(10), 833. https://doi.org/10.15407/ujpe66.10.833



Fields and elementary particles