A tour of high energy physics: from quantum field theory to Higgs coupling measurements at the LHC

This document summarizes work in theoretical and experimental high-energy physics completed as part of the author's doctoral studies. Beginning with an overview of the relevant backgrounds, the motivation for this doctoral research is explored through discussion of the current state of particle physics and many of the unanswered questions driving research in this field. Emphasis is placed on providing context for doctoral research to readers outside of the particle physics community. Theoretical work from early PhD studies is summarized, exploring the continuity of scalar quantum fields and studying a novel toy field theory with intriguing nonlinear wave solutions. Recent research in experimental particle physics is presented in further detail, and a measurement is presented in collaboration with the CMS experiment located at CERN. This measurement quantifies the strength of interaction between the top quark and Higgs boson, obtaining a Yukawa coupling 0.24 value of $Y$$_{t}$ = 1.16$_{-0.36}^{+0.24}$ relative to the standard model.