Kostylenko Y. O. Field-theoretical description of deuteron and positronium properties in the clothed-particle representation. – Qualification scientific paper, manuscript.
Thesis for a Doctor of Philosophy degree in Physics and Mathematics: Speciality 01.04.02 “Theoretical physics” (104 – Physics and Astronomy). – A.I. Akhiezer Institute for Theoretical Physics of the National Science Center “Kharkiv Institute of Physics and Technology” NAS of Ukraine, – National Science Center “Kharkiv Institute of Physics and Technology” NAS of Ukraine, Kharkiv, 2024.
This research is devoted to applications of the concept of the so-called clothed particles, put forward in the relativistic quantum field theory by O. Greenberg and S. Schweber, that survived its second birth in the 70s owing to the work by M. Shirokov, and developed then by the collaboration of the Akhiezer Institute for Theoretical Physics (Kharkiv, Ukraine), Padova Division of the National Institute for Nuclear Physics (Padova, Italy) and Institute of Electrophysics and Radiation Technologies (Kharkiv, Ukraine).
Recall that by using the method of unitary clothing transformations the total field Hamiltonian H and other operators of great physical meaning (e.g., the Lorentz boosts and current density operators), initially depending on the creation and destruction operators for the “bare” particles, can be expressed through a new set of their “clothed” counterparts. It is achieved via special unitary clothing transformations that remain the Hamiltonian intact. In the course of the clothing procedure a large amount of virtual processes associated in our case with the meson absorption/emission, the nucleon-antinucleon pair annihilation/production and other cloud effects turn out to be accumulated in the creation (destruction) operators for the clothed (physical) particles. Such a feature reflects the most significant distinction between the concepts of clothed and bare particles.
The first section is focused on the explanation of the concept of clothed particles. The historical background of the method of unitary clothing transformations is given and an intermediate representation of the bare particles with physical masses is introduced. We show how one can transfer to the clothed-particle representation, determine certain constraints imposed on the corresponding clothing transformations and meet them. We are also addressing the well-known field models of interacting nucleons, mesons, electrons and photons with Yukawa-type couplings. Finally, we consider the links between our approach and the in(out) formalism by Lehmann, Symanzik and Zimmermann.
In the second section, following the common recipes when removing the so-called “bad” terms within the clothing procedure, we show our calculations of the fermion mass shifts in the system of interacting nucleon and ρ meson fields as well as in the quantum electrodynamics. The method of unitary clothing transformations allows us to get rid of divergent terms associated with the renormalization problem directly in the Hamiltonian. Thus, they can no longer appear in the S-matrix. The mass shifts are expressed through the corresponding three-dimensional integrals whose integrands depend on certain invariant combinations of the relevant three-momenta. Our results are proved to be particle-momentum independent and compared with ones obtained via the Feynman technique. Following the approach proposed, mass renormalization is considered simultaneously with the construction of a new family of interactions between the clothed particles (quasiparticles in the clothed-particle representation).
In the third section, starting with the field Hamiltonian of interacting mesons (π, η, ρ, ω, δ, σ) and nucleons, we show an original way to build up a new family of electromagnetic meson exchange current operators via the method of unitary clothing transformations. Being introduced in such a way they do not depend on the choice of states with which we calculate the matrix elements. The new expressions for meson exchange currents have been compared with ones derived in the previous explorations. An effective technique of ensuring gauge independence based on the generalization of Siegertʼs theorem is proposed.
In the fourth section, we have used the currents derived to describe the deuteron electromagnetic properties. The deuteron in the instant form of relativistic dynamics for such a model is the bound state of the clothed neutron and proton on their mass shells. This fact allows us to get rid of non-relativistic uncertainties inherent in the conventional approaches in the past. In particular, we do not need to “invent” any off-shell models for the γN, γπ, γρ, etc. vertices. Special attention is paid to the deuteron eigenvalue problem and finding the proper deuteron states in a moving frame. We have computed the deuteron magnetic form factor taking into account both one-body and two-body currents.
