Gauge covariance of the fermion Schwinger–Dyson equation in QED

Jia, Shaoyang; Pennington, M. R.

doi:10.1016/j.physletb.2017.03.032

Title: Gauge covariance of the fermion Schwinger–Dyson equation in QED

Abstract

Any practical application of the Schwinger–Dyson equations to the study of n-point Green's functions in a strong coupling field theory requires truncations. In the case of QED, the gauge covariance, governed by the Landau–Khalatnikov–Fradkin transformations (LKFT), provides a unique constraint on such truncation. Here, by using a spectral representation for the massive fermion propagator in QED, we are able to show that the constraints imposed by the LKFT are linear operations on the spectral densities. We formally define these group operations and show with a couple of examples how in practice they provide a straightforward way to test the gauge covariance of any viable truncation of the Schwinger–Dyson equation for the fermion 2-point function.

Authors:: Jia, Shaoyang; Pennington, M. R.

Publication Date:: Thu Jun 01 00:00:00 EDT 2017

Research Org.:: Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Nuclear Physics (NP)

OSTI Identifier:: 1405533

Alternate Identifier(s):: OSTI ID: 1356976

Report Number(s):: JLAB-THY-16-2355; DOE/OR/23177-3950; arXiv:1610.06001
Journal ID: ISSN 0370-2693; S0370269317302204; PII: S0370269317302204

Grant/Contract Number:: AC05-06OR23177; CRC 110; FPA2013-40483-P; FIS2014-51948-C2-2-P; SEV-2014-0398; PROMETEOII/2014/0068

Resource Type:: Published Article

Journal Name:: Physics Letters B

Additional Journal Information:: Journal Name: Physics Letters B Journal Volume: 769 Journal Issue: C; Journal ID: ISSN 0370-2693

Publisher:: Elsevier

Country of Publication:: Netherlands

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Citation Formats


                    Jia, Shaoyang, and Pennington, M. R. Gauge covariance of the fermion Schwinger–Dyson equation in QED.  Netherlands: N. p., 2017. 
Web.  doi:10.1016/j.physletb.2017.03.032.

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                    Jia, Shaoyang, & Pennington, M. R. Gauge covariance of the fermion Schwinger–Dyson equation in QED.  Netherlands.  https://doi.org/10.1016/j.physletb.2017.03.032

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                    Jia, Shaoyang, and Pennington, M. R. Thu .  
"Gauge covariance of the fermion Schwinger–Dyson equation in QED".  Netherlands.  https://doi.org/10.1016/j.physletb.2017.03.032.

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@article{osti_1405533,

  title        = {Gauge covariance of the fermion Schwinger–Dyson equation in QED},

  author       = {Jia, Shaoyang and Pennington, M. R.},

  abstractNote = {Any practical application of the Schwinger–Dyson equations to the study of n-point Green's functions in a strong coupling field theory requires truncations. In the case of QED, the gauge covariance, governed by the Landau–Khalatnikov–Fradkin transformations (LKFT), provides a unique constraint on such truncation. Here, by using a spectral representation for the massive fermion propagator in QED, we are able to show that the constraints imposed by the LKFT are linear operations on the spectral densities. We formally define these group operations and show with a couple of examples how in practice they provide a straightforward way to test the gauge covariance of any viable truncation of the Schwinger–Dyson equation for the fermion 2-point function.},

  doi          = {10.1016/j.physletb.2017.03.032},

  journal      = {Physics Letters B},

  number       = C,

  volume       = 769,

  place        = {Netherlands},

  year         = {Thu Jun 01 00:00:00 EDT 2017},

  month        = {Thu Jun 01 00:00:00 EDT 2017}

}

Copy to clipboard

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Works referencing / citing this record:

Landau-Khalatnikov-Fradkin transformation and the mystery of even $ζ$ -values in Euclidean massless correlators
journal, November 2019

Kotikov, A. V.; Teber, S.
Physical Review D, Vol. 100, Issue 10
DOI: 10.1103/physrevd.100.105017

Exact solutions to the fermion propagator Schwinger-Dyson equation in Minkowski space with on-shell renormalization for quenched QED
journal, August 2017

Jia, Shaoyang; Pennington, M. R.
Physical Review D, Vol. 96, Issue 3
DOI: 10.1103/physrevd.96.036021

Fresh look at the Abelian and non-Abelian Landau-Khalatnikov-Fradkin transformations
journal, April 2018

De Meerleer, T.; Dudal, D.; Sorella, S. P.
Physical Review D, Vol. 97, Issue 7
DOI: 10.1103/physrevd.97.074017

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Title: Gauge covariance of the fermion Schwinger–Dyson equation in QED

Abstract

Citation Formats

Landau-Khalatnikov-Fradkin transformation and the mystery of even ζ -values in Euclidean massless correlators journal, November 2019

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