Landau-Khalatnikov-Fradkin transformation for the fermion propagator in QED in arbitrary dimensions

Jia, Shaoyang; Pennington, Michael R.

doi:10.1103/PhysRevD.95.076007

Title: Landau-Khalatnikov-Fradkin transformation for the fermion propagator in QED in arbitrary dimensions

Abstract

Here, we explore the dependence of fermion propagators on the covariant gauge fixing parameter in quantum electrodynamics (QED) with the number of spacetime dimensions kept explicit. Gauge covariance is controlled by the the Landau -Khalatnikov-Fradkin transformation (LKFT). Utilizing its group nature, the LKFT for a fermion propagator in Minkowski space is solved exactly. The special scenario of 3D has been used to test claims made for general cases. When renormalized correctly, the simplification of the LKFT in 4D has been achieved with the help of fractional calculus.

Authors:

Jia, Shaoyang ^[1]; Pennington, Michael R. ^[2]

College of William and Mary, Williamsburg, VA (United States)
College of William and Mary, Williamsburg, VA (United States); Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)

Publication Date:: Mon Apr 10 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:: 1357536

Alternate Identifier(s):: OSTI ID: 1351048

Report Number(s):: JLAB-THY-16-2356; DOE/OR/23177-3951; arXiv:1610.06436; IPPP/16/94
Journal ID: ISSN 2470-0010; PRVDAQ

Grant/Contract Number:: AC05-06OR23177

Resource Type:: Accepted Manuscript

Journal Name:: Physical Review D

Additional Journal Information:: Journal Volume: 95; Journal Issue: 7; Journal ID: ISSN 2470-0010

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Citation Formats


                    Jia, Shaoyang, and Pennington, Michael R. Landau-Khalatnikov-Fradkin transformation for the fermion propagator in QED in arbitrary dimensions.  United States: N. p., 2017. 
Web.  doi:10.1103/PhysRevD.95.076007.

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                    Jia, Shaoyang, & Pennington, Michael R. Landau-Khalatnikov-Fradkin transformation for the fermion propagator in QED in arbitrary dimensions.  United States.  https://doi.org/10.1103/PhysRevD.95.076007

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                    Jia, Shaoyang, and Pennington, Michael R. Mon .  
"Landau-Khalatnikov-Fradkin transformation for the fermion propagator in QED in arbitrary dimensions".  United States.  https://doi.org/10.1103/PhysRevD.95.076007.  https://www.osti.gov/servlets/purl/1357536.

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@article{osti_1357536,

  title        = {Landau-Khalatnikov-Fradkin transformation for the fermion propagator in QED in arbitrary dimensions},

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

  abstractNote = {Here, we explore the dependence of fermion propagators on the covariant gauge fixing parameter in quantum electrodynamics (QED) with the number of spacetime dimensions kept explicit. Gauge covariance is controlled by the the Landau -Khalatnikov-Fradkin transformation (LKFT). Utilizing its group nature, the LKFT for a fermion propagator in Minkowski space is solved exactly. The special scenario of 3D has been used to test claims made for general cases. When renormalized correctly, the simplification of the LKFT in 4D has been achieved with the help of fractional calculus.},

  doi          = {10.1103/PhysRevD.95.076007},

  journal      = {Physical Review D},

  number       = 7,

  volume       = 95,

  place        = {United States},

  year         = {Mon Apr 10 00:00:00 EDT 2017},

  month        = {Mon Apr 10 00:00:00 EDT 2017}

}

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Works referenced in this record:

Dynamical mass generation in unquenched QED using the Dyson-Schwinger equations
journal, March 2015

Kızılersü, Ayşe; Sizer, Tom; Pennington, Michael R.
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How gauge covariance of the fermion and boson propagators in QED constrain the effective fermion-boson vertex
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Jia, Shaoyang; Pennington, M. R.
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Aslam, M. Jamil; Bashir, A.; Gutiérrez-Guerrero, L. X.
Physical Review D, Vol. 93, Issue 7
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Landau-Khalatnikov-Fradkin transformations and the fermion propagator in quantum electrodynamics
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Bashir, A.; Raya, A.
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On the gauge parameter dependence of QED
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Sonoda, Hidenori
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Landau-Khalatnikov-Fradkin transformations in reduced quantum electrodynamics
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Ahmad, A.; Cobos-Martínez, J. J.; Concha-Sánchez, Y.
Physical Review D, Vol. 93, Issue 9
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Ward identities and charge renormalization of the Yang-Mills field
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Taylor, J. C.
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Extended BRS symmetry and gauge independence in on-shell renormalization schemes
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Alavian, S.; Steele, T. G.
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Ward identities in gauge theories
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Gauge Dependence of the Wave-Function Renormalization Constant in Quantum Electrodynamics
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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

Exact Solutions to the Fermion Propagator Schwinger-Dyson Equation in Minkowski space with on-shell Renormalization for Quenched QED
text, January 2017

Jia, Shaoyang; Pennington, M. R.
arXiv
DOI: 10.48550/arxiv.1705.04523

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Title: Landau-Khalatnikov-Fradkin transformation for the fermion propagator in QED in arbitrary dimensions

Abstract

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