Renormalization and gauge invariance in quantum electrodynamics
Autor(a) principal: | |
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Data de Publicação: | 1970 |
Outros Autores: | , |
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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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 |
dc.type.driver.fl_str_mv |
Estrangeiro info:eu-repo/semantics/article |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
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article |
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publishedVersion |
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http://hdl.handle.net/10183/206335 |
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0550-3213 |
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000148229 |
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http://hdl.handle.net/10183/206335 |
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eng |
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eng |
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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info:eu-repo/semantics/openAccess |
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openAccess |
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