Renormalization and gauge invariance in quantum electrodynamics

Detalhes bibliográficos
Autor(a) principal: Maris, Theodor August Johannes
Data de Publicação: 1970
Outros Autores: Dillenburg, Darcy, Jacob, Gerhard
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UFRGS
Texto Completo: http://hdl.handle.net/10183/206335
Resumo: The connection between the field theory and the perturbation expansion of quantum electrodynamics is studied. As a starting point the usual Lagrangian is taken but with bare electron mass and the renormalization constant Z3 set equal to zero. This theory is essentially equivalent to the usual one; however, it does not contain any constant of nature and is dilatational and gauge invariant, both invariances being spontaneously broken. The various limiting procedures implied by the differentiation, the multiplication and the renormalization of the field operators in the Lagrangian are combined in a gauge invariant way to a single limit. Propagator equations are derived which are the usual renormalized ones, except for: (i) a natural cancellation of the quadratic divergence of the vacuum polarization; (ii) the presence of an effective cutoff at p ≈ ϵ−1; (iii) the replacement of the renormalization constants Z1 and Z2 by one gauge dependent function Z(ϵ2); (iv) the limit ϵ → 0 which has to be taken. The value Z(0) corresponds to the usual constants Z1 and Z2. It is expected that in general Z(0) = 0, but this poses no problem in the present formulation. It is argued that the function Z(ϵ2), which is determined by the equations, may render the vacuum polarization finite. One may eliminate the renormalization function from the propagator equations and then perform the limit ϵ → 0; this results in the usual perturbation series. However, the renormalization function is essential for an understanding of the high momentum behaviour and of the relation between the field theory and the perturbation expansion.
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spelling Maris, Theodor August JohannesDillenburg, DarcyJacob, Gerhard2020-02-28T04:07:22Z19700550-3213http://hdl.handle.net/10183/206335000148229The connection between the field theory and the perturbation expansion of quantum electrodynamics is studied. As a starting point the usual Lagrangian is taken but with bare electron mass and the renormalization constant Z3 set equal to zero. This theory is essentially equivalent to the usual one; however, it does not contain any constant of nature and is dilatational and gauge invariant, both invariances being spontaneously broken. The various limiting procedures implied by the differentiation, the multiplication and the renormalization of the field operators in the Lagrangian are combined in a gauge invariant way to a single limit. Propagator equations are derived which are the usual renormalized ones, except for: (i) a natural cancellation of the quadratic divergence of the vacuum polarization; (ii) the presence of an effective cutoff at p ≈ ϵ−1; (iii) the replacement of the renormalization constants Z1 and Z2 by one gauge dependent function Z(ϵ2); (iv) the limit ϵ → 0 which has to be taken. The value Z(0) corresponds to the usual constants Z1 and Z2. It is expected that in general Z(0) = 0, but this poses no problem in the present formulation. It is argued that the function Z(ϵ2), which is determined by the equations, may render the vacuum polarization finite. One may eliminate the renormalization function from the propagator equations and then perform the limit ϵ → 0; this results in the usual perturbation series. However, the renormalization function is essential for an understanding of the high momentum behaviour and of the relation between the field theory and the perturbation expansion.application/pdfengNuclear Physics. B. Amsterdam. Vol. B18, no. 1 (May 1970), p. 366-389Física nuclearEletrodinamica quanticaRenormalizacaoInvarianciaQuebra espontanea de simetriasRenormalization and gauge invariance in quantum electrodynamicsEstrangeiroinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/openAccessreponame:Repositório Institucional da UFRGSinstname:Universidade Federal do Rio Grande do Sul (UFRGS)instacron:UFRGSTEXT000148229.pdf.txt000148229.pdf.txtExtracted Texttext/plain58710http://www.lume.ufrgs.br/bitstream/10183/206335/2/000148229.pdf.txt2f8e6e1bf1cc609e0d7bb5ff85fb2ca0MD52ORIGINAL000148229.pdfTexto completo (inglês)application/pdf1215389http://www.lume.ufrgs.br/bitstream/10183/206335/1/000148229.pdff494deb00b17c2de08d6a4d4cc187a7eMD5110183/2063352020-02-29 04:21:50.685259oai:www.lume.ufrgs.br:10183/206335Repositório de PublicaçõesPUBhttps://lume.ufrgs.br/oai/requestopendoar:2020-02-29T07:21:50Repositório Institucional da UFRGS - Universidade Federal do Rio Grande do Sul (UFRGS)false
dc.title.pt_BR.fl_str_mv Renormalization and gauge invariance in quantum electrodynamics
title Renormalization and gauge invariance in quantum electrodynamics
spellingShingle Renormalization and gauge invariance in quantum electrodynamics
Maris, Theodor August Johannes
Física nuclear
Eletrodinamica quantica
Renormalizacao
Invariancia
Quebra espontanea de simetrias
title_short Renormalization and gauge invariance in quantum electrodynamics
title_full Renormalization and gauge invariance in quantum electrodynamics
title_fullStr Renormalization and gauge invariance in quantum electrodynamics
title_full_unstemmed Renormalization and gauge invariance in quantum electrodynamics
title_sort Renormalization and gauge invariance in quantum electrodynamics
author Maris, Theodor August Johannes
author_facet Maris, Theodor August Johannes
Dillenburg, Darcy
Jacob, Gerhard
author_role author
author2 Dillenburg, Darcy
Jacob, Gerhard
author2_role author
author
dc.contributor.author.fl_str_mv Maris, Theodor August Johannes
Dillenburg, Darcy
Jacob, Gerhard
dc.subject.por.fl_str_mv Física nuclear
Eletrodinamica quantica
Renormalizacao
Invariancia
Quebra espontanea de simetrias
topic Física nuclear
Eletrodinamica quantica
Renormalizacao
Invariancia
Quebra espontanea de simetrias
description The connection between the field theory and the perturbation expansion of quantum electrodynamics is studied. As a starting point the usual Lagrangian is taken but with bare electron mass and the renormalization constant Z3 set equal to zero. This theory is essentially equivalent to the usual one; however, it does not contain any constant of nature and is dilatational and gauge invariant, both invariances being spontaneously broken. The various limiting procedures implied by the differentiation, the multiplication and the renormalization of the field operators in the Lagrangian are combined in a gauge invariant way to a single limit. Propagator equations are derived which are the usual renormalized ones, except for: (i) a natural cancellation of the quadratic divergence of the vacuum polarization; (ii) the presence of an effective cutoff at p ≈ ϵ−1; (iii) the replacement of the renormalization constants Z1 and Z2 by one gauge dependent function Z(ϵ2); (iv) the limit ϵ → 0 which has to be taken. The value Z(0) corresponds to the usual constants Z1 and Z2. It is expected that in general Z(0) = 0, but this poses no problem in the present formulation. It is argued that the function Z(ϵ2), which is determined by the equations, may render the vacuum polarization finite. One may eliminate the renormalization function from the propagator equations and then perform the limit ϵ → 0; this results in the usual perturbation series. However, the renormalization function is essential for an understanding of the high momentum behaviour and of the relation between the field theory and the perturbation expansion.
publishDate 1970
dc.date.issued.fl_str_mv 1970
dc.date.accessioned.fl_str_mv 2020-02-28T04:07:22Z
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dc.relation.ispartof.pt_BR.fl_str_mv Nuclear Physics. B. Amsterdam. Vol. B18, no. 1 (May 1970), p. 366-389
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