A&S Graduate Studies
[PAST EVENT] Shaoyang Jia: Physics Dissertation Defense
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 the first principle, 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.
Bio: Shaoyang Jia was born in Houma, a small town in Shanxi province of China. In the year 2008, he went to college in Xiamen University as a mechanical engineering student. One year later he realized that engineering did not suit his interests and transferred to physics. He graduated with a Bachelor?s degree in June 2012, after which he came to pursue a Ph.D at William & Mary. He started working on the Schwinger-Dyson equation approach to nonperturbative field theories with Michael Pennington since 2013.