How gauge covariance of the fermion and boson propagators in QED constrain the effective fermion-boson vertex
Abstract
In this paper, we derive the gauge covariance requirement imposed on the QED fermion-photon three-point function within the framework of a spectral representation for fermion propagators. When satisfied, such requirement ensures solutions to the fermion propagator Schwinger-Dyson equation (SDE) in any covariant gauge with arbitrary numbers of spacetime dimensions to be consistent with the Landau-Khalatnikov-Fradkin transformation (LKFT). The general result has been verified by the special cases of three and four dimensions. Additionally, we present the condition that ensures the vacuum polarization is independent of the gauge parameter. Finally, as an illustration, we show how the gauge technique dimensionally regularized in four dimensions does not satisfy the covariance requirement.
- Authors:
-
- College of William and Mary, Williamsburg, VA (United States). Physics Dept.
- College of William and Mary, Williamsburg, VA (United States). Physics Dept.; Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States). Theory Center
- Publication Date:
- Research Org.:
- Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); College of William and Mary, Williamsburg, VA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Nuclear Physics (NP)
- OSTI Identifier:
- 1335374
- Alternate Identifier(s):
- OSTI ID: 1335196
- Report Number(s):
- JLAB-THY-16-2373; DOE/OR-23177-3975
Journal ID: ISSN 2470-0010
- Grant/Contract Number:
- AC05-06OR23177
- Resource Type:
- Journal Article: Accepted Manuscript
- Journal Name:
- Physical Review D
- Additional Journal Information:
- Journal Volume: 94; Journal Issue: 11; 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, M. R. How gauge covariance of the fermion and boson propagators in QED constrain the effective fermion-boson vertex. United States: N. p., 2016.
Web. doi:10.1103/PhysRevD.94.116004.
Jia, Shaoyang, & Pennington, M. R. How gauge covariance of the fermion and boson propagators in QED constrain the effective fermion-boson vertex. United States. https://doi.org/10.1103/PhysRevD.94.116004
Jia, Shaoyang, and Pennington, M. R. 2016.
"How gauge covariance of the fermion and boson propagators in QED constrain the effective fermion-boson vertex". United States. https://doi.org/10.1103/PhysRevD.94.116004. https://www.osti.gov/servlets/purl/1335374.
@article{osti_1335374,
title = {How gauge covariance of the fermion and boson propagators in QED constrain the effective fermion-boson vertex},
author = {Jia, Shaoyang and Pennington, M. R.},
abstractNote = {In this paper, we derive the gauge covariance requirement imposed on the QED fermion-photon three-point function within the framework of a spectral representation for fermion propagators. When satisfied, such requirement ensures solutions to the fermion propagator Schwinger-Dyson equation (SDE) in any covariant gauge with arbitrary numbers of spacetime dimensions to be consistent with the Landau-Khalatnikov-Fradkin transformation (LKFT). The general result has been verified by the special cases of three and four dimensions. Additionally, we present the condition that ensures the vacuum polarization is independent of the gauge parameter. Finally, as an illustration, we show how the gauge technique dimensionally regularized in four dimensions does not satisfy the covariance requirement.},
doi = {10.1103/PhysRevD.94.116004},
url = {https://www.osti.gov/biblio/1335374},
journal = {Physical Review D},
issn = {2470-0010},
number = 11,
volume = 94,
place = {United States},
year = {Mon Dec 12 00:00:00 EST 2016},
month = {Mon Dec 12 00:00:00 EST 2016}
}
Web of Science
Works referenced in this record:
Generating fermion mass in four-dimensional quenched QED
journal, September 1992
- Curtis, D. C.; Pennington, M. R.
- Physical Review D, Vol. 46, Issue 6
Dynamical mass generation in unquenched QED using the Dyson-Schwinger equations
journal, March 2015
- Kızılersü, Ayşe; Sizer, Tom; Pennington, Michael R.
- Physical Review D, Vol. 91, Issue 6
Analysis of a quenched lattice-QCD dressed-quark propagator
journal, July 2003
- Bhagwat, M. S.; Pichowsky, M. A.; Roberts, C. D.
- Physical Review C, Vol. 68, Issue 1
Regularization-independent study of renormalized nonperturbative quenched QED
journal, April 2002
- Kızılersü, Ayşe; Sizer, Tom; Williams, Anthony G.
- Physical Review D, Vol. 65, Issue 8
Critical coupling in strong QED with weak gauge dependence
journal, June 1994
- Atkinson, D.; Bloch, J. C. R.; Gusynin, V. P.
- Physics Letters B, Vol. 329, Issue 1
Transverse Vector Vertex Function and Transverse Ward–Takahashi Relations in QED
journal, July 2006
- Han-Xin, He
- Communications in Theoretical Physics, Vol. 46, Issue 1
Nonperturbative study of the fermion propagator in quenched QED in covariant gauges using a renormalizable truncation of the Schwinger-Dyson equation
journal, November 1993
- Curtis, D. C.; Pennington, M. R.
- Physical Review D, Vol. 48, Issue 10
Phase structure of unquenched QED with four-fermion interaction
journal, March 1991
- Kondo, Kei-Ichi
- Nuclear Physics B, Vol. 351, Issue 1-2
Renormalizable Electrodynamics of Vector Mesons
journal, May 1963
- Salam, Abdus
- Physical Review, Vol. 130, Issue 3
Critical number of flavors in QED
journal, February 2011
- Bashir, A.; Calcaneo-Roldan, C.; Gutiérrez-Guerrero, L. X.
- Physical Review D, Vol. 83, Issue 3
Strongly-coupled unquenched propagators using Schwinger-Dyson equations
journal, August 2013
- Kızılersü, Ayşe; Sizer, Tom; Williams, Anthony G.
- Physical Review D, Vol. 88, Issue 4
Structure of the neutral pion and its electromagnetic transition form factor
journal, April 2016
- Raya, Khépani; Chang, Lei; Bashir, Adnan
- Physical Review D, Vol. 93, Issue 7
Renormalizable Electrodynamics of Scalar and Vector Mesons. II
journal, September 1964
- Salam, Abdus; Delbourgo, Robert
- Physical Review, Vol. 135, Issue 6B
Confinement phenomenology in the Bethe-Salpeter equation
journal, March 2003
- Bhagwat, M. S.; Pichowsky, M. A.; Tandy, P. C.
- Physical Review D, Vol. 67, Issue 5
Collective Perspective on Advances in Dyson—Schwinger Equation QCD
journal, July 2012
- Bashir, Adnan; Chang, Lei; Cloët, Ian C.
- Communications in Theoretical Physics, Vol. 58, Issue 1
Bethe-Salpeter study of vector meson masses and decay constants
journal, October 1999
- Maris, Pieter; Tandy, Peter C.
- Physical Review C, Vol. 60, Issue 5
Nucleon and Roper electromagnetic elastic and transition form factors
journal, February 2012
- Wilson, D. J.; Cloët, I. C.; Chang, L.
- Physical Review C, Vol. 85, Issue 2
Transverse Ward–Takahashi identity for the fermion-boson vertex in gauge theories
journal, May 2000
- He, Hanxin; Khanna, F. C.; Takahashi, Y.
- Physics Letters B, Vol. 480, Issue 1-2
condensate for light quarks beyond the chiral limit
journal, February 2007
- Williams, R.; Fischer, C. S.; Pennington, M. R.
- Physics Letters B, Vol. 645, Issue 2-3
A gauge covariant approximation to quantum electrodynamics
journal, June 1977
- Delbourgo, R.; West, P.
- Journal of Physics A: Mathematical and General, Vol. 10, Issue 6
Gauge-independent chiral symmetry breaking in quenched QED
journal, December 1994
- Bashir, A.; Pennington, M. R.
- Physical Review D, Vol. 50, Issue 12
Schwinger-Dyson equation for massless vector theory and the absence of a fermion pole
journal, December 1976
- Fukuda, Reijiro; Kugo, Taichiro
- Nuclear Physics B, Vol. 117, Issue 1
Analytic structure of the full fermion propagator in quenched and unquenched QED
journal, September 1994
- Maris, P.
- Physical Review D, Vol. 50, Issue 6
Imaging Dynamical Chiral-Symmetry Breaking: Pion Wave Function on the Light Front
journal, March 2013
- Chang, Lei; Cloët, I. C.; Cobos-Martinez, J. J.
- Physical Review Letters, Vol. 110, Issue 13
Gauge covariance and the gauge technique
journal, April 1981
- Delbourgo, R.; Keck, B. W.; Parker, C. N.
- Journal of Physics A: Mathematical and General, Vol. 14, Issue 4
An Identity in Quantum Electrodynamics
journal, April 1950
- Ward, J. C.
- Physical Review, Vol. 78, Issue 2
Strong Coupling Unquenched QED. II: Numerical Study
journal, October 1992
- Kondo, K. -i.; Nakatani, H.
- Progress of Theoretical Physics, Vol. 88, Issue 4
Truncating the Schwinger-Dyson equations: How multiplicative renormalizability and the Ward identity restrict the three-point vertex in QED
journal, December 1990
- Curtis, D. C.; Pennington, M. R.
- Physical Review D, Vol. 42, Issue 12
Building the full fermion-photon vertex of QED by imposing multiplicative renormalizability of the Schwinger-Dyson equations for the fermion and photon propagators
journal, June 2009
- Kızılersü, Ayşe; Pennington, Michael R.
- Physical Review D, Vol. 79, Issue 12
Revealing Dressed Quarks via the Proton’s Charge Distribution
journal, September 2013
- Cloët, Ian C.; Roberts, Craig D.; Thomas, Anthony W.
- Physical Review Letters, Vol. 111, Issue 10
Dyson-Schwinger equations and their application to hadronic physics
journal, January 1994
- Roberts, Craig D.; Williams, Anthony G.
- Progress in Particle and Nuclear Physics, Vol. 33
Gauge Properties of Propagators in Quantum Electrodynamics
journal, January 1960
- Zumino, Bruno
- Journal of Mathematical Physics, Vol. 1, Issue 1
Hadron Physics and QCD: Just the Basic Facts.
journal, July 2015
- Roberts, Crag D.
- Journal of Physics: Conference Series, Vol. 630
Running Masses in the Nucleon and its Resonances
conference, May 2016
- Roberts, Craig D.
- Proceedings of the 10th International Workshop on the Physics of Excited Nucleons (NSTAR2015)
Regularization-independent studies of nonperturbative field theory
journal, February 2001
- Kızılersü, Ayşe; Schreiber, Andreas W.; Williams, Anthony G.
- Physics Letters B, Vol. 499, Issue 3-4
Bethe–Salpeter bound-state structure in Minkowski space
journal, August 2016
- Gutierrez, C.; Gigante, V.; Frederico, T.
- Physics Letters B, Vol. 759
Modified Perturbation Method for Spinor Electrodynamics
journal, September 1964
- Strathdee, J.
- Physical Review, Vol. 135, Issue 6B
Dynamical chiral symmetry breaking and the fermion–gauge-boson vertex
journal, April 2012
- Bashir, A.; Bermudez, R.; Chang, L.
- Physical Review C, Vol. 85, Issue 4
Critical Number of Flavours in QED
text, January 2011
- Bashir, A.; Calcaneo-Roldan, C.; Gutiérrez-Guerrero, L. X.
- arXiv
Nucleon and Roper electromagnetic elastic and transition form factors
text, January 2011
- Wilson, D. J.; Cloet, I. C.; Chang, L.
- arXiv
Imaging dynamical chiral symmetry breaking: pion wave function on the light front
text, January 2013
- Chang, Lei; Cloet, I. C.; Cobos-Martinez, J. J.
- arXiv
Regularization-independent study of renormalized non-perturbative quenched QED
text, January 2001
- Kizilersu, A.; Sizer, T.; Williams, A. G.
- arXiv
Study of relativistic bound states for scalar theories in Bethe-Salpeter and Dyson-Schwinger formalism
text, January 2001
- Sauli, Vladimir; Adam, Jiri
- arXiv
Dyson-Schwinger Equations and the Application to Hadronic Physics
text, January 1994
- Roberts, C. D.; Williams, A. G.
- arXiv
Gauge independent Chiral Symmetry Breaking in Quenched QED
text, January 1994
- Bashir, A.; Pennington, M. R.
- arXiv
Solving the Bethe-Salpeter equation for bound states of scalar theories in Minkowski space
text, January 1997
- Kusaka, Kensuke; Simpson, Ken; Williams, Anthony G.
- arXiv
Quantum anomaly of the transverse Ward-Takahashi relation for the axial-vector vertex
text, January 2002
- He, Han-xin
- arXiv
Bethe-Salpeter Study of Vector Meson Masses and Decay Constants
text, January 1999
- Maris, Pieter; Tandy, Peter. C.
- arXiv
Works referencing / citing this record:
Landau-Khalatnikov-Fradkin transformation and the mystery of even -values in Euclidean massless correlators
journal, November 2019
- Kotikov, A. V.; Teber, S.
- Physical Review D, Vol. 100, Issue 10
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
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