Drastic violation of the U-matrix boundary condition by quantum-field theoretical on-shell renormalization and a new consistent renormalization concept involving bound-state problems

J. Seke

Physica A: Statistical Mechanics and its Applications, 2002, vol. 312, issue 3, 392-420

Abstract: By generalizing the Gell-Mann–Low formula and applying the self-consistent projection-operator method, developed a decade ago by the present author, a connecting equation between the fermion propagator (involving the interaction with the quantum electromagnetic field in the presence of an external field) and the U-matrix elements, being valid to any order of the fermion–photon interaction, is derived. After proving rigorously, the drastic violation of the U-matrix boundary condition (U(t,t)=1) by the conventional on-shell renormalization of the fermion propagator (removal of free-fermion pole and residue corrections), the absolute necessity for the formulation of a new renormalization concept becomes self-evident. This latter is achieved in the present paper by elaborating a consistent renormalization procedure, based on the self-consistent projection-operator method (which, unlike the standard perturbation method, guarantees the consistency of the applied approximation to any order as to the strength of the interaction). The new complete renormalization, unlike the conventional one, removes completely the experimentally unobservable free-electron Dyson self-energy from the fermion propagator. By applying the new concept, for the first time, consistently renormalized contributions (up to the fourth order) to the bound-electron self-energy function with the corresponding Feynman diagrams are derived.

Keywords: Renormalization; Dyson self-energy; Self-consistent projection-operator method; Gell-Mann–Low formula; U-matrix; Bound-state problems; Feynman diagrams (search for similar items in EconPapers)
Date: 2002
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437102008658
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:312:y:2002:i:3:p:392-420

DOI: 10.1016/S0378-4371(02)00865-8

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().