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

Jia, Shaoyang; Pennington, M. R.

doi:10.1103/PhysRevD.96.036021

Title: Exact solutions to the fermion propagator Schwinger-Dyson equation in Minkowski space with on-shell renormalization for quenched QED

Journal Article · Tue Aug 01 00:00:00 EDT 2017 · Physical Review D

DOI:https://doi.org/10.1103/PhysRevD.96.036021· OSTI ID:1392567

Jia, Shaoyang ^[1]; Pennington, M. 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); Glasgow Univ. (United Kingdom)

With the introduction of a spectral representation, the Schwinger-Dyson equation (SDE) for the fermion propagator is formulated in Minkowski space in QED. After imposing the on-shell renormalization conditions, analytic solutions for the fermion propagator spectral functions are obtained in four dimensions with a renormalizable version of the Gauge Technique anzatz for the fermion-photon vertex in the quenched approximation in the Landau gauge. Despite the limitations of this model, having an explicit solution provides a guiding example of the fermion propagator with the correct analytic structure. The Padé approximation for the spectral functions is also investigated.

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

Sponsoring Organization:: USDOE

Grant/Contract Number:: AC05-06OR23177

OSTI ID:: 1392567

Alternate ID(s):: OSTI ID: 1377967

Report Number(s):: JLAB-THY-17-2465; arXiv:1705.04523; PRVDAQ

Journal Information:: Physical Review D, Vol. 96, Issue 3; ISSN 2470-0010

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 7 works

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References (28)

Resummations in the Bloch-Nordsieck model Jakovác, A.; Mati, P. Physical Review D, Vol. 85, Issue 8 https://doi.org/10.1103/PhysRevD.85.085006	journal	April 2012
Analysis of a quenched lattice-QCD dressed-quark propagator Bhagwat, M. S.; Pichowsky, M. A.; Roberts, C. D. Physical Review C, Vol. 68, Issue 1 https://doi.org/10.1103/PhysRevC.68.015203	journal	July 2003
Explanation and prediction of observables using continuum strong QCD Cloët, Ian C.; Roberts, Craig D. Progress in Particle and Nuclear Physics, Vol. 77 https://doi.org/10.1016/j.ppnp.2014.02.001	journal	July 2014
Renormalizable Electrodynamics of Vector Mesons Salam, Abdus Physical Review, Vol. 130, Issue 3 https://doi.org/10.1103/PhysRev.130.1287	journal	May 1963
On the gauge dependence of spectral functions Delbourgo, R.; Keck, B. W. Journal of Physics A: Mathematical and General, Vol. 13, Issue 2 https://doi.org/10.1088/0305-4470/13/2/032	journal	February 1980
On the Green's functions of quantized fields. I Schwinger, J. Proceedings of the National Academy of Sciences, Vol. 37, Issue 7 https://doi.org/10.1073/pnas.37.7.452	journal	July 1951
Strongly-coupled unquenched ${QED}_{4}$ propagators using Schwinger-Dyson equations Kızılersü, Ayşe; Sizer, Tom; Williams, Anthony G. Physical Review D, Vol. 88, Issue 4 https://doi.org/10.1103/PhysRevD.88.045008	journal	August 2013
Renormalizable Electrodynamics of Scalar and Vector Mesons. II Salam, Abdus; Delbourgo, Robert Physical Review, Vol. 135, Issue 6B https://doi.org/10.1103/PhysRev.135.B1398	journal	September 1964
On the Green's functions of quantized fields. II Schwinger, J. Proceedings of the National Academy of Sciences, Vol. 37, Issue 7 https://doi.org/10.1073/pnas.37.7.455	journal	July 1951
Spectral function of the Bloch-Nordsieck model at finite temperature Jakovác, A.; Mati, P. Physical Review D, Vol. 87, Issue 12 https://doi.org/10.1103/PhysRevD.87.125007	journal	June 2013
Collective Perspective on Advances in Dyson—Schwinger Equation QCD Bashir, Adnan; Chang, Lei; Cloët, Ian C. Communications in Theoretical Physics, Vol. 58, Issue 1 https://doi.org/10.1088/0253-6102/58/1/16	journal	July 2012
Gauge covariance of the fermion Schwinger–Dyson equation in QED Jia, Shaoyang; Pennington, M. R. Physics Letters B, Vol. 769 https://doi.org/10.1016/j.physletb.2017.03.032	journal	June 2017
How gauge covariance of the fermion and boson propagators in QED constrain the effective fermion-boson vertex Jia, Shaoyang; Pennington, M. R. Physical Review D, Vol. 94, Issue 11 https://doi.org/10.1103/PhysRevD.94.116004	journal	December 2016
Validating the 2PI resummation: The Bloch-Nordsieck example Jakovác, A.; Mati, P. Physical Review D, Vol. 90, Issue 4 https://doi.org/10.1103/PhysRevD.90.045038	journal	August 2014
Analytic properties of the vertex function in gauge theories. I Ball, James S.; Chiu, Ting-Wai Physical Review D, Vol. 22, Issue 10 https://doi.org/10.1103/PhysRevD.22.2542	journal	November 1980
A gauge covariant approximation to quantum electrodynamics Delbourgo, R.; West, P. Journal of Physics A: Mathematical and General, Vol. 10, Issue 6 https://doi.org/10.1088/0305-4470/10/6/024	journal	June 1977
On the quark-gluon vertex and quark-ghost kernel: combining lattice simulations with Dyson-Schwinger equations Rojas, E.; de Melo, J. P. B. C.; El-Bennich, B. Journal of High Energy Physics, Vol. 2013, Issue 10 https://doi.org/10.1007/JHEP10(2013)193	journal	October 2013
Gauge covariance and the gauge technique Delbourgo, R.; Keck, B. W.; Parker, C. N. Journal of Physics A: Mathematical and General, Vol. 14, Issue 4 https://doi.org/10.1088/0305-4470/14/4/020	journal	April 1981
Landau-Khalatnikov-Fradkin transformation for the fermion propagator in QED in arbitrary dimensions Jia, Shaoyang; Pennington, M. R. Physical Review D, Vol. 95, Issue 7 https://doi.org/10.1103/PhysRevD.95.076007	journal	April 2017
Truncating the Schwinger-Dyson equations: How multiplicative renormalizability and the Ward identity restrict the three-point vertex in QED Curtis, D. C.; Pennington, M. R. Physical Review D, Vol. 42, Issue 12 https://doi.org/10.1103/PhysRevD.42.4165	journal	December 1990
Building the full fermion-photon vertex of QED by imposing multiplicative renormalizability of the Schwinger-Dyson equations for the fermion and photon propagators Kızılersü, Ayşe; Pennington, Michael R. Physical Review D, Vol. 79, Issue 12 https://doi.org/10.1103/PhysRevD.79.125020	journal	June 2009
The $S$ Matrix in Quantum Electrodynamics Dyson, F. J. Physical Review, Vol. 75, Issue 11 https://doi.org/10.1103/PhysRev.75.1736	journal	June 1949
Baryons as relativistic three-quark bound states Eichmann, Gernot; Sanchis-Alepuz, Hèlios; Williams, Richard Progress in Particle and Nuclear Physics, Vol. 91 https://doi.org/10.1016/j.ppnp.2016.07.001	journal	November 2016
Analytic Structure of the Landau-Gauge Gluon Propagator Strauss, Stefan; Fischer, Christian S.; Kellermann, Christian Physical Review Letters, Vol. 109, Issue 25 https://doi.org/10.1103/PhysRevLett.109.252001	journal	December 2012
Modified Perturbation Method for Spinor Electrodynamics Strathdee, J. Physical Review, Vol. 135, Issue 6B https://doi.org/10.1103/PhysRev.135.B1428	journal	September 1964
Spectral function of the Bloch-Nordsieck model at finite temperature Jakovac, A.; Mati, P. arXiv https://doi.org/10.48550/arxiv.1301.1803	text	January 2013
Explanation and Prediction of Observables using Continuum Strong QCD Cloet, Ian C.; Roberts, Craig D. arXiv https://doi.org/10.48550/arxiv.1310.2651	text	January 2013
Gauge covariance of the fermion Schwinger-Dyson equation in QED Jia, Shaoyang; Pennington, M. R. arXiv https://doi.org/10.48550/arxiv.1610.06001	text	January 2016

Cited By (3)

Quark Propagator in Minkowski Space Solis, E. L.; Costa, C. S. R.; Luiz, V. V. Few-Body Systems, Vol. 60, Issue 3 https://doi.org/10.1007/s00601-019-1517-9	journal	June 2019
Landau-Khalatnikov-Fradkin transformation and the mystery of even $ζ$ -values in Euclidean massless correlators Kotikov, A. V.; Teber, S. Physical Review D, Vol. 100, Issue 10 https://doi.org/10.1103/physrevd.100.105017	journal	November 2019
Scattering amplitudes and contour deformations Eichmann, Gernot; Duarte, Pedro; Peña, M. T. arXiv https://doi.org/10.48550/arxiv.1907.05402	text	January 2019

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Title: Exact solutions to the fermion propagator Schwinger-Dyson equation in Minkowski space with on-shell renormalization for quenched QED

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