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

Available for download on Saturday, October 06, 2018

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