Gauge covariance of the fermion Schwinger–Dyson equation in QED
Any practical application of the Schwinger–Dyson equations to the study of npoint 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 2point function.
 Authors:

^{[1]};
^{[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:
 Report Number(s):
 JLABTHY162355; DOE/OR/231773950; arXiv:1610.06001
Journal ID: ISSN 03702693; PII: S0370269317302204
 Grant/Contract Number:
 AC0506OR23177; CRC 110; FPA201340483P; FIS201451948C22P; SEV20140398; PROMETEOII/2014/0068
 Type:
 Published Article
 Journal Name:
 Physics Letters. Section B
 Additional Journal Information:
 Journal Volume: 769; Journal Issue: C; Journal ID: ISSN 03702693
 Publisher:
 Elsevier
 Research Org:
 Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
 Sponsoring Org:
 USDOE Office of Science (SC), Nuclear Physics (NP) (SC26)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
 OSTI Identifier:
 1405533
 Alternate Identifier(s):
 OSTI ID: 1356976
Jia, Shaoyang, and Pennington, Michael R. Gauge covariance of the fermion Schwinger–Dyson equation in QED. United States: N. p.,
Web. doi:10.1016/j.physletb.2017.03.032.
Jia, Shaoyang, & Pennington, Michael R. Gauge covariance of the fermion Schwinger–Dyson equation in QED. United States. doi:10.1016/j.physletb.2017.03.032.
Jia, Shaoyang, and Pennington, Michael R. 2017.
"Gauge covariance of the fermion Schwinger–Dyson equation in QED". United States.
doi:10.1016/j.physletb.2017.03.032.
@article{osti_1405533,
title = {Gauge covariance of the fermion Schwinger–Dyson equation in QED},
author = {Jia, Shaoyang and Pennington, Michael R.},
abstractNote = {Any practical application of the Schwinger–Dyson equations to the study of npoint 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 2point function.},
doi = {10.1016/j.physletb.2017.03.032},
journal = {Physics Letters. Section B},
number = C,
volume = 769,
place = {United States},
year = {2017},
month = {3}
}