Gauge covariance of the fermion Schwinger–Dyson equation in QED

Journal Article · Thu Jun 01 00:00:00 EDT 2017 · Physics Letters B

DOI:https://doi.org/10.1016/j.physletb.2017.03.032· OSTI ID:1405533

Jia, Shaoyang; Pennington, M. R.

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.

• Research Organization: Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
• Sponsoring Organization: USDOE Office of Science (SC), Nuclear Physics (NP)
• Grant/Contract Number: AC05-06OR23177; CRC 110; FPA2013-40483-P; FIS2014-51948-C2-2-P; SEV-2014-0398; PROMETEOII/2014/0068
• OSTI ID: 1405533
• Alternate ID(s): OSTI ID: 1356976
• Report Number(s): JLAB-THY-16-2355; DOE/OR/23177-3950; arXiv:1610.06001; S0370269317302204; PII: S0370269317302204
• Journal Information: Physics Letters B, Journal Name: Physics Letters B Vol. 769 Journal Issue: C; ISSN 0370-2693
• Publisher: Elsevier
• Country of Publication: Netherlands
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS