ORCID ID
0000-0002-8226-2279
Date Awarded
2017
Document Type
Dissertation
Degree Name
Doctor of Philosophy (Ph.D.)
Department
Physics
Advisor
Michael Pennington
Committee Member
Konstantinos Orginos
Committee Member
Seth Aubin
Committee Member
Ian Cloet
Committee Member
Anatoly Radyushkin
Abstract
The Schwinger-Dyson equations (SDEs) are coupled integral equations for the Green's functions of a quantum field theory (QFT). The SDE approach is the analytic nonperturbative method for solving strongly coupled QFTs. When applied to QCD, this approach, also based on first principles, is the analytic alternative to lattice QCD. However, the SDEs for the n-point Green's functions involves (n+1)-point Green's functions (sometimes (n+2)-point functions as well). Therefore any practical method for solving this infinitely coupled system of equations requires a truncation scheme. When considering strongly coupled QED as a modeling of QCD, naive truncation schemes violate various principles of the gauge theory. These principles include gauge invariance, gauge covariance, and multiplicative renormalizability. The combination of dimensional regularization with the spectral representation of propagators results in a tractable formulation of a truncation scheme for the SDEs of QED propagators, which has the potential to preserve the aforementioned principles and renders solutions obtainable in the Minkowski space. This truncation scheme is the main result of this dissertation.
DOI
http://dx.doi.org/doi:10.21220/S2CD44
Rights
© The Author
Recommended Citation
Jia, Shaoyang, "Formulating Schwinger-Dyson Equations for Qed Propagators in Minkowski Space" (2017). Dissertations, Theses, and Masters Projects. William & Mary. Paper 1516639559.
http://dx.doi.org/doi:10.21220/S2CD44
